From 39c0b7787db20d5f6273754cd61fb4a86fb29497 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Tue, 18 Feb 2025 12:52:00 +0100 Subject: [PATCH 01/18] init xspace converter --- extras/ome_n3lo/convert_ome_xspace.py | 91 +++++++++++++++++++++++++++ 1 file changed, 91 insertions(+) create mode 100644 extras/ome_n3lo/convert_ome_xspace.py diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py new file mode 100644 index 000000000..622b089f3 --- /dev/null +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -0,0 +1,91 @@ + +import numpy as np +from click import progressbar +from eko.mellin import Path +from ekore.harmonics import cache as c +from ekore.operator_matrix_elements.unpolarized.space_like import as3 +from scipy import integrate + +XGRID = np.geomspace(1e-6, 1, 500) # 500 +"""X-grid.""" + +LOG = 0 +"""Matching threshold displaced ?""" + +MAP_ENTRIES = { + "gg": (0, 0), + "gq": (0, 1), + "qg": (1, 0), + "qq": (1, 1), + "Hg": (2, 0), + "Hq": (2, 1), + "gH": (0, 2), + "HH": (2, 2), + "qq_ns": (0, 0), +} + + +def compute_ome(nf, n, is_singlet): + """Get the correct ome from eko.""" + cache = c.reset() + if is_singlet: + return as3.A_singlet(n, cache, nf, L=0) + else: + return as3.A_ns(n, cache, nf, L=0) + + +def compute_xspace_ome(entry, nf, x_grid=XGRID): + """Compute the x-space transition matrix element, returns A^3(x).""" + mellin_cut = 5e-2 + is_singlet = "ns" not in entry + + def integrand(u, x): + """Mellin inversion integrand.""" + path = Path(u, np.log(x), is_singlet) + integrand = path.prefactor * x ** (-path.n) * path.jac + if integrand == 0.0: + return 0.0 + + ome_n = compute_ome(nf, path.n, is_singlet) + idx1, idx2 = MAP_ENTRIES[entry] + ome_n = ome_n[idx1, idx2] + + # recombine everything + return np.real(ome_n * integrand) + + ome_x = [] + print(f"Computing operator matrix element {entry} @ pto: 3") + # loop on xgrid + with progressbar(x_grid) as bar: + for x in bar: + if x == 1: + ome_x.append(0) + continue + res = integrate.quad( + lambda u: integrand(u, x), + 0.5, + 1.0 - mellin_cut, + epsabs=1e-12, + epsrel=1e-6, + limit=200, + full_output=1, + )[0] + ome_x.append(res) + + return np.array(ome_x) + + +def save_files(entry, nf, ome_x, xgrid=XGRID): + """Write the space reuslt in a txt file.""" + with open(f"x_space/A_{entry}_nf{nf}.txt", "w") as file: + for x, a in zip(xgrid, ome_x): + file.write(f"{x}\t{a}\n") + + +if __name__ == "__main__": + nf = 3 # nf = 3,4,5. + # non diagonal temrms + for k in ["gq", "qg", "Hg", "Hq"]: + result = compute_xspace_ome(k, nf) + save_files(k, nf, result) + # ["ns", "gg", "qq",]: From 8f6c81f91d07064feacd40f4ab2368a2267dcc19 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 12:54:09 +0100 Subject: [PATCH 02/18] improve saving methods --- extras/ome_n3lo/.gitignore | 3 +++ extras/ome_n3lo/convert_ome_xspace.py | 18 ++++++++---------- extras/{ => ome_n3lo}/n3lo_matching.tar.gz | Bin 3 files changed, 11 insertions(+), 10 deletions(-) create mode 100644 extras/ome_n3lo/.gitignore rename extras/{ => ome_n3lo}/n3lo_matching.tar.gz (100%) diff --git a/extras/ome_n3lo/.gitignore b/extras/ome_n3lo/.gitignore new file mode 100644 index 000000000..978f5fa29 --- /dev/null +++ b/extras/ome_n3lo/.gitignore @@ -0,0 +1,3 @@ +*.pdf +*.f +*.txt diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 622b089f3..3cb0739d9 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -1,4 +1,3 @@ - import numpy as np from click import progressbar from eko.mellin import Path @@ -6,7 +5,7 @@ from ekore.operator_matrix_elements.unpolarized.space_like import as3 from scipy import integrate -XGRID = np.geomspace(1e-6, 1, 500) # 500 +XGRID = np.geomspace(1e-6, 1, 100) # 500 """X-grid.""" LOG = 0 @@ -54,7 +53,7 @@ def integrand(u, x): return np.real(ome_n * integrand) ome_x = [] - print(f"Computing operator matrix element {entry} @ pto: 3") + print(f"Computing operator matrix element {entry} @ pto: 3, nf: {nf}") # loop on xgrid with progressbar(x_grid) as bar: for x in bar: @@ -75,17 +74,16 @@ def integrand(u, x): return np.array(ome_x) -def save_files(entry, nf, ome_x, xgrid=XGRID): +def save_files(entry, ome_x, xgrid=XGRID): """Write the space reuslt in a txt file.""" - with open(f"x_space/A_{entry}_nf{nf}.txt", "w") as file: - for x, a in zip(xgrid, ome_x): - file.write(f"{x}\t{a}\n") + fname = f"x_space/A_{entry}.txt" + np.savetxt(fname, np.concatenate(([xgrid], np.array(ome_x))).T) if __name__ == "__main__": - nf = 3 # nf = 3,4,5. # non diagonal temrms for k in ["gq", "qg", "Hg", "Hq"]: - result = compute_xspace_ome(k, nf) - save_files(k, nf, result) + # TODO: here we should use the lower patch nf, correct ?? + result = [compute_xspace_ome(k, nf) for nf in [3, 4, 5]] + save_files(k, result) # ["ns", "gg", "qq",]: diff --git a/extras/n3lo_matching.tar.gz b/extras/ome_n3lo/n3lo_matching.tar.gz similarity index 100% rename from extras/n3lo_matching.tar.gz rename to extras/ome_n3lo/n3lo_matching.tar.gz From 8b1e00cc818648dea5d31bb6ab0f3af70c14c79f Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 13:14:13 +0100 Subject: [PATCH 03/18] adding large-x expansion --- extras/ome_n3lo/largex_limit.py | 38 + .../notebooks/Agg_Aqq_largex_expansion.nb | 1147 +++++++++++++ extras/ome_n3lo/notebooks/Xspace.m | 1423 +++++++++++++++++ .../{ => notebooks}/n3lo_matching.tar.gz | Bin 4 files changed, 2608 insertions(+) create mode 100644 extras/ome_n3lo/largex_limit.py create mode 100644 extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb create mode 100644 extras/ome_n3lo/notebooks/Xspace.m rename extras/ome_n3lo/{ => notebooks}/n3lo_matching.tar.gz (100%) diff --git a/extras/ome_n3lo/largex_limit.py b/extras/ome_n3lo/largex_limit.py new file mode 100644 index 000000000..b83a34fda --- /dev/null +++ b/extras/ome_n3lo/largex_limit.py @@ -0,0 +1,38 @@ +"""This file contains the large-N limit of the diagonal Matrix elements. + +The expansions are obtained using the notebook Agg_Aqq_largex_expansion.nb. + +We note that: + * the limit og :math:`A_{qq}` is the same for non-singlet like and singlet-like expansions. + I.e. the local and singular part are the same + * the :math:`A_{qq,ps}` temr is vanishing in the large-x limit, i.e. it's only regular. +""" +from ekore.harmonics import S1 + + +def Aqq_asymptotic(n, nf): + """The N3LO quark-to-quark transition matrix element large-N limit.""" + return ( + (20.36251906478134 - 3.4050138869326796 * nf) * S1(n) + - 72.36717694258661 + + 3.11448410587291 * nf + ) + + +def Agg_asymptotic(n, nf): + """The N3LO gluon-to-gluon transition matrix element large-N limit. + Follwing :cite:`Ablinger:2022wbb`: + * the fist part contains the limit of eq. 2.6 (except for :math:`a_{gg}^{(3)}`) + * the second part comes from eq. 4.6 and 4.7. + """ + Agg_asy_incomplete = ( + (-669.1554507291286 + 41.84286985333757 * nf) * S1(n) + - 565.4465327471261 + + 28.65462637880661 * nf + ) + agg_asy = ( + 49.5041510989361 * (-14.442649813264895 + nf) * S1(n) + + 619.2420126046355 + - 17.52475977636971 * nf + ) + return agg_asy + Agg_asy_incomplete diff --git a/extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb b/extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb new file mode 100644 index 000000000..51a05cd8e --- /dev/null +++ b/extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb @@ -0,0 +1,1147 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 12.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 41517, 1139] +NotebookOptionsPosition[ 38434, 1083] +NotebookOutlinePosition[ 38826, 1099] +CellTagsIndexPosition[ 38783, 1096] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ +Cell[BoxData[ + RowBox[{"Exit", "[", "]"}]], "Input", + CellChangeTimes->{{3.948945578061242*^9, 3.948945579446208*^9}}, + CellLabel->"In[20]:=",ExpressionUUID->"b15860d2-997b-48de-9a18-81b5e0a2b6ce"], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{"here", " ", "=", " ", + RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + ";"}], "\n", + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + ";"}]}], "Code", + CellChangeTimes->{{3.9489469906313868`*^9, 3.948946991034669*^9}, { + 3.948954007032343*^9, + 3.948954039800639*^9}},ExpressionUUID->"cf4d06e7-cd27-4f38-a624-\ +1bf2aace7b0c"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + StyleBox["Sigma", + FontColor->RGBColor[1, 0, 0]], + RowBox[{" ", + RowBox[{ + RowBox[{ + RowBox[{"-", " ", "A"}], " ", "summation", " ", "package", " ", "by", + " ", "Carsten", " ", "Schneider"}], " ", "\[LongDash]", " ", + RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", + RowBox[{"V", " ", "2.86", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"June", " ", "15"}], ",", " ", "2021"}], ")"}], " "}]}]}], + ButtonBox[ + StyleBox["Help", "Hyperlink", + FontVariations->{"Underline"->True}], + Appearance->{Automatic, None, "Normal", Automatic}, + ButtonData:>{"", ""}, + ButtonFunction:>Sigma`Version`Private`SigmaHelp[], + Evaluator->Automatic]}]], "Print", + CellFrame->0.5, + CellChangeTimes->{3.948945587247348*^9}, + FontColor->RGBColor[0, 0, 0], + Background->RGBColor[0.796887, 0.789075, 0.871107], + ButtonBoxOptions->{ + Active->True},ExpressionUUID->"ee915aa4-2754-4223-bf26-787baf2d6893"], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"HarmonicSums", " ", "by", " ", "Jakob", " ", "Ablinger"}], " ", + "\[LongDash]", " ", + RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", + RowBox[{"Version", " ", "1.0"}]}], + RowBox[{"(", + RowBox[{ + RowBox[{"30", "/", "03"}], "/", "21"}], ")"}]}], + ButtonBox[ + StyleBox["Help", "Hyperlink", + FontVariations->{"Underline"->True}], + Appearance->{Automatic, None, "Normal", Automatic}, + ButtonFunction:>HarmonicSums`Private`HarmonicSumsHelp[], + Evaluator->Automatic]}]], "Print", + CellFrame->0.5, + CellChangeTimes->{3.948945693340869*^9}, + FontColor->GrayLevel[0.], + Background->RGBColor[0.796887, 0.789075, 0.871107], + ButtonBoxOptions->{ + Active->True},ExpressionUUID->"10592614-5c1d-48ee-b699-00d5f161866b"] +}, Open ]] +}, Open ]], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"here", " ", "=", " ", + RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\n", + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], + "\n"}], "\n", + RowBox[{ + RowBox[{"QCDConst", " ", "=", " ", + RowBox[{"{", + RowBox[{ + RowBox[{"CA", " ", "\[Rule]", " ", "3"}], ",", " ", + RowBox[{"TF", " ", "\[Rule]", " ", + RowBox[{"1", "/", "2"}]}], ",", " ", + RowBox[{"CF", " ", "\[Rule]", " ", + RowBox[{"4", "/", "3"}]}], ",", " ", + RowBox[{"B4", " ", "\[Rule]", " ", + RowBox[{ + RowBox[{ + RowBox[{"-", "4"}], " ", "z2", " ", + RowBox[{ + RowBox[{"Log", "[", "2", "]"}], "^", "2"}]}], " ", "+", " ", + RowBox[{ + RowBox[{"2", "/", "3"}], " ", + RowBox[{ + RowBox[{"Log", "[", "2", "]"}], "^", "4"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"13", "/", "2"}], " ", "z4"}], " ", "+", " ", + RowBox[{"16", " ", "li4half"}]}]}]}], "}"}]}], ";"}]}], "Code", + CellChangeTimes->{{3.948945446657963*^9, 3.948945479177684*^9}, { + 3.948945522327042*^9, 3.948945522782468*^9}, {3.9489482445131893`*^9, + 3.948948271795343*^9}, {3.9489505412478857`*^9, 3.9489505417142143`*^9}, { + 3.9489510312362022`*^9, 3.948951079482356*^9}, {3.94895111925445*^9, + 3.948951119583748*^9}}, + CellLabel-> + "In[217]:=",ExpressionUUID->"3e9423b7-e0d4-4093-b3ce-955024eadbb5"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{"Matching", " ", "conditions", " ", "symbols"}], " ", "*)"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"AggQ123N", ";"}], "\[IndentingNewLine]", + RowBox[{"AqqQPS3", ";"}], "\[IndentingNewLine]", + RowBox[{"AqqQNS123N", ";"}]}]}]], "Input", + CellChangeTimes->{{3.9489455067904367`*^9, 3.94894552825358*^9}, { + 3.948950547119001*^9, + 3.948950561491927*^9}},ExpressionUUID->"38ac9fa3-fd03-4c80-97d5-\ +f0a3587299c5"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"GetLargeXLimit", "[", + RowBox[{"expr_", ",", " ", "order_", ",", " ", "Log_"}], "]"}], " ", ":=", + " ", + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", "expansion", "}"}], ",", "\n", "\t", + RowBox[{ + RowBox[{"expansion", " ", "=", " ", + RowBox[{"SExpansion", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"expr", " ", "/.", " ", + RowBox[{ + RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "Log"}]}], " ", "/.", + " ", "QCDConst"}], " ", "//", " ", "ReduceToBasis"}], ",", " ", + "N", ",", " ", "order"}], "]"}]}], ";", "\n", "\t", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"expansion", ",", + RowBox[{"LG", "[", "N", "]"}]}], "]"}], + RowBox[{"LG", "[", "N", "]"}]}], ",", " ", + RowBox[{ + RowBox[{"expansion", " ", "-", + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"expansion", ",", + RowBox[{"LG", "[", "N", "]"}]}], "]"}], + RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", "Simplify"}]}], + "}"}]}]}], "\n", "]"}]}]], "Code", + CellChangeTimes->{{3.948948538528637*^9, 3.948948649446475*^9}, { + 3.948948844433375*^9, 3.948949008788335*^9}}, + CellLabel-> + "In[222]:=",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", + RowBox[{ + RowBox[{ + "Some", " ", "checks", " ", "that", " ", "the", " ", "thing", " ", "is", + " ", "working", " ", "as", " ", "it", " ", "should"}], " ", "..."}], " ", + "*)"}], "\n", + RowBox[{ + RowBox[{"GetLargeXLimit", "[", + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQPS3", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", "\n", + RowBox[{"GetLargeXLimit", "[", + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", + RowBox[{"Coefficient", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], " ", "/.", " ", + RowBox[{ + RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", + " ", "QCDConst"}], " ", "//", " ", "Expand"}], ",", + RowBox[{"S", "[", + RowBox[{"1", ",", "N"}], "]"}]}], "]"}], "\n", + RowBox[{ + RowBox[{"Series", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], "/.", " ", + RowBox[{ + RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", + "QCDConst"}], ",", " ", + RowBox[{"{", + RowBox[{"N", ",", "Infinity", ",", "0"}], "}"}]}], " ", "]"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"S", "[", + RowBox[{"2", ",", "N"}], "]"}], "\[Rule]", " ", "z2"}], ",", " ", + RowBox[{ + RowBox[{"S", "[", + RowBox[{"3", ",", "N"}], "]"}], "\[Rule]", " ", "z3"}]}], + "}"}]}]}]}]], "Code", + CellChangeTimes->{{3.948949013421583*^9, 3.9489490753518457`*^9}, { + 3.948949822620695*^9, 3.948949849941022*^9}, {3.948950000521757*^9, + 3.948950014801219*^9}}, + CellLabel-> + "In[223]:=",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}]], "Output", + CellChangeTimes->{ + 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9}, + CellLabel-> + "Out[223]=",ExpressionUUID->"932538e5-3fcc-4d6a-8839-992b3e2af928"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"-", + FractionBox[ + RowBox[{"448", " ", + RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ",", + RowBox[{ + FractionBox["1", "27"], " ", + RowBox[{"(", + RowBox[{"73", "+", + RowBox[{"80", " ", "z2"}], "-", + RowBox[{"48", " ", "z3"}]}], ")"}]}]}], "}"}]], "Output", + CellChangeTimes->{ + 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948950002023658*^9, 3.948951086434144*^9, 3.9489511458553877`*^9}, + CellLabel-> + "Out[224]=",ExpressionUUID->"0ccc496d-ebd3-4707-91cd-5192d14850da"], + +Cell[BoxData[ + RowBox[{"-", + FractionBox["448", "81"]}]], "Output", + CellChangeTimes->{ + 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145856818*^9}, + CellLabel-> + "Out[225]=",ExpressionUUID->"580512ef-0d2c-49df-9693-7668a37ccce8"], + +Cell[BoxData["\<\"Cannot load 'SExpTab2'. Proceed without precomputed \ +expansions.\"\>"], "Print", + CellChangeTimes->{3.948951086526724*^9, 3.948951145878625*^9}, + CellLabel-> + "During evaluation of \ +In[223]:=",ExpressionUUID->"c498f812-14d3-4a68-9da2-c8e933e5afc4"], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"-", + FractionBox["448", "81"]}], " ", + RowBox[{"S", "[", + RowBox[{"1", ",", "N"}], "]"}]}], "+", + RowBox[{"(", + InterpretationBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + FractionBox["73", "27"], "+", + FractionBox[ + RowBox[{"80", " ", "z2"}], "27"], "-", + FractionBox[ + RowBox[{"16", " ", "z3"}], "9"]}], ")"}], "+", + InterpretationBox[ + SuperscriptBox[ + RowBox[{"O", "[", + FractionBox["1", "N"], "]"}], "1"], + SeriesData[N, + DirectedInfinity[1], {}, 0, 1, 1], + Editable->False]}], + SeriesData[N, + DirectedInfinity[1], { + Rational[73, 27] + Rational[80, 27] $CellContext`z2 + + Rational[-16, 9] $CellContext`z3}, 0, 1, 1], + Editable->False], ")"}]}]], "Output", + CellChangeTimes->{ + 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951146118248*^9}, + CellLabel-> + "Out[226]=",ExpressionUUID->"918f1b3f-684b-41b7-bb1e-09e8ac524de5"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + "Pure", " ", "singlet", " ", "term", " ", "is", " ", "convergent", " ", + "as", " ", "it", " ", "should"}], " ", "*)"}], "\n", + RowBox[{"SExpansion", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQPS3", ",", " ", "as", ",", " ", "3"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "->", " ", "1"}]}], + " ", "/.", " ", + RowBox[{ + RowBox[{"L", "[", "M", "]"}], " ", "->", " ", "0"}]}], ",", " ", "N", + ",", " ", "1"}], "]"}]}]], "Code", + CellChangeTimes->{{3.948950247009811*^9, 3.948950270110826*^9}}, + CellLabel-> + "In[227]:=",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], + +Cell[BoxData["0"], "Output", + CellChangeTimes->{3.948950271429709*^9, 3.9489510906139727`*^9, + 3.948951149651967*^9}, + CellLabel-> + "Out[227]=",ExpressionUUID->"d3bc2ff3-a6a1-4b6c-985e-9651a6d3b117"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{"qqNS", " ", "asy"}], " ", "*)"}], "\n", + RowBox[{"qqNSasy", " ", "=", " ", + RowBox[{"GetLargeXLimit", "[", + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}]}]}]], "Code", + CellChangeTimes->{{3.948950027207466*^9, 3.948950027437483*^9}, { + 3.9489501048247967`*^9, 3.948950153621386*^9}, 3.948951106558529*^9}, + CellLabel-> + "In[228]:=",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{ + FractionBox["141640", "2187"], "+", + FractionBox[ + RowBox[{"1024", " ", "li4half"}], "27"], "+", + FractionBox[ + RowBox[{"128", " ", + SuperscriptBox["ln2", "4"]}], "81"], "-", + FractionBox[ + RowBox[{"24064", " ", "NF"}], "2187"], "+", + FractionBox[ + RowBox[{"6592", " ", "z2"}], "81"], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox["z2", "2"]}], "15"], "-", + FractionBox[ + RowBox[{"280", " ", "z3"}], "27"], "+", + FractionBox[ + RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", + FractionBox[ + RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"-", + RowBox[{ + FractionBox["1", "3645"], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"132700", "+", + RowBox[{"51840", " ", "li4half"}], "+", + RowBox[{"2160", " ", + SuperscriptBox["ln2", "4"]}], "-", + RowBox[{"11830", " ", "NF"}], "-", + RowBox[{"11760", " ", "z2"}], "-", + RowBox[{"12960", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "-", + RowBox[{"960", " ", "NF", " ", "z2"}], "+", + RowBox[{"6144", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"1152", " ", "NF", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"291105", " ", "z3"}], "+", + RowBox[{"3840", " ", "NF", " ", "z3"}], "-", + RowBox[{"107280", " ", "z2", " ", "z3"}], "-", + RowBox[{"166860", " ", "z4"}], "+", + RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", + CellChangeTimes->{{3.9489500247139473`*^9, 3.948950039220125*^9}, + 3.948950111791774*^9, 3.948950157878325*^9, 3.94895110422303*^9, + 3.948951163201816*^9}, + CellLabel-> + "Out[228]=",ExpressionUUID->"14f874a8-730a-4bee-bb0b-f93be4c938f2"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"qqNS", " ", "asy"}], ",", " ", + RowBox[{"for", " ", "singlet", " ", "like"}]}], " ", "*)"}], "\n", + RowBox[{ + RowBox[{"qqSasy", " ", "=", " ", + RowBox[{"GetLargeXLimit", "[", + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + RowBox[{"(*", " ", + RowBox[{ + "check", " ", "that", " ", "the", " ", "2", " ", "are", " ", "the", " ", + "same"}], " ", "*)"}], "\n", + RowBox[{"qqNSasy", " ", "-", " ", "qqSasy"}]}]}]], "Code", + CellChangeTimes->{{3.9489500926863003`*^9, 3.9489501123045464`*^9}, { + 3.948950162196804*^9, 3.948950206961136*^9}}, + CellLabel-> + "In[231]:=",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{ + FractionBox["141640", "2187"], "+", + FractionBox[ + RowBox[{"1024", " ", "li4half"}], "27"], "+", + FractionBox[ + RowBox[{"128", " ", + SuperscriptBox["ln2", "4"]}], "81"], "-", + FractionBox[ + RowBox[{"24064", " ", "NF"}], "2187"], "+", + FractionBox[ + RowBox[{"6592", " ", "z2"}], "81"], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox["z2", "2"]}], "15"], "-", + FractionBox[ + RowBox[{"280", " ", "z3"}], "27"], "+", + FractionBox[ + RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", + FractionBox[ + RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"-", + RowBox[{ + FractionBox["1", "3645"], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"132700", "+", + RowBox[{"51840", " ", "li4half"}], "+", + RowBox[{"2160", " ", + SuperscriptBox["ln2", "4"]}], "-", + RowBox[{"11830", " ", "NF"}], "-", + RowBox[{"11760", " ", "z2"}], "-", + RowBox[{"12960", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "-", + RowBox[{"960", " ", "NF", " ", "z2"}], "+", + RowBox[{"6144", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"1152", " ", "NF", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"291105", " ", "z3"}], "+", + RowBox[{"3840", " ", "NF", " ", "z3"}], "-", + RowBox[{"107280", " ", "z2", " ", "z3"}], "-", + RowBox[{"166860", " ", "z4"}], "+", + RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", + CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { + 3.948950204161031*^9, 3.948950211058175*^9}, 3.948951193419348*^9}, + CellLabel-> + "Out[231]=",ExpressionUUID->"31a2b1bc-7efa-42df-bd24-d103791159cf"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}]], "Output", + CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { + 3.948950204161031*^9, 3.948950211058175*^9}, 3.9489511934214067`*^9}, + CellLabel-> + "Out[232]=",ExpressionUUID->"c46fc0e1-a4fd-40d6-8949-8d1c6b684e2a"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{ + StyleBox[ + RowBox[{"(", "*"}]], " ", + RowBox[{ + RowBox[{"Gluon", " ", "Limit"}], ",", " ", + RowBox[{ + "aggQ3", " ", "expansion", " ", "is", " ", "added", " ", "later"}]}], + " ", + StyleBox[ + RowBox[{"*", ")"}]]}], "Code"], + StyleBox["\n", "Code"], + RowBox[{ + RowBox[{ + StyleBox["ggasy", "Code"], + StyleBox[" ", "Code"], + StyleBox["=", "Code"], + StyleBox[" ", "Code"], + RowBox[{ + StyleBox["GetLargeXLimit", "Code"], "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AggQ123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", + RowBox[{"aggQ3", " ", "\[Rule]", " ", "0"}]}], " ", "/.", " ", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + RowBox[{"(*", " ", + RowBox[{ + RowBox[{ + RowBox[{ + "Here", " ", "now", " ", "we", " ", "need", " ", "to", " ", "add", " ", + "also", " ", "the", " ", "aggQ3", " ", + RowBox[{"piece", ":", " ", "https", ":"}]}], "//", + RowBox[{ + RowBox[{ + RowBox[{"arxiv", ".", "org"}], "/", "pdf"}], "/", "2211.05462"}]}], + ",", " ", + RowBox[{"see", " ", "ancillary", " ", "file", " ", + RowBox[{"Xspace", ".", "m"}]}]}], " ", "*)"}], "\n", + RowBox[{"(*", " ", + RowBox[{"Form", " ", "eq", " ", "4.6"}], " ", "*)"}], "\n", + RowBox[{ + RowBox[{"aggQ3DEL", " ", "=", " ", + RowBox[{ + RowBox[{"Coefficient", "[", "\n", "\t\t", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"CF", "*", + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "1478"}], "/", "81"}], " ", "+", " ", + RowBox[{"NF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "1942"}], "/", "81"}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"20", "*", "z2"}], ")"}], "/", "3"}]}], ")"}]}], + " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"88", "*", "z2"}], ")"}], "/", "3"}], " ", "-", " ", + RowBox[{"7", "*", "z3"}]}], ")"}]}], " ", "+", " ", "\n", + " ", + RowBox[{ + RowBox[{"(", + RowBox[{"64", "*", + RowBox[{"TF", "^", "3"}], "*", "z3"}], ")"}], "/", "27"}], " ", + "+", " ", + RowBox[{ + RowBox[{"CF", "^", "2"}], "*", "TF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"274", "/", "9"}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"95", "*", "z3"}], ")"}], "/", "3"}]}], ")"}]}], " ", + "+", " ", "\n", " ", + RowBox[{"CA", "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", + RowBox[{ + RowBox[{"2587", "/", "135"}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"572", "*", "z2"}], ")"}], "/", "27"}], " ", "+", + " ", + RowBox[{"NF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "178"}], "/", "9"}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"196", "*", "z2"}], ")"}], "/", "27"}]}], ")"}]}], + " ", "-", " ", "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"291", "*", "z3"}], ")"}], "/", "10"}]}], ")"}]}], + " ", "+", " ", + RowBox[{"CF", "*", "TF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"16541", "/", "162"}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"64", "*", "B4"}], ")"}], "/", "3"}], " ", "+", + " ", + RowBox[{"52", "*", "z2"}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"2617", "*", "z3"}], ")"}], "/", "12"}], " ", "+", + " ", "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"128", "*", "z4"}], ")"}], "/", "3"}]}], ")"}]}]}], + ")"}]}], " ", "+", " ", + RowBox[{ + RowBox[{"CA", "^", "2"}], "*", "TF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"34315", "/", "324"}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"32", "*", "B4"}], ")"}], "/", "3"}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"20435", "*", "z3"}], ")"}], "/", "216"}], " ", "+", + " ", "\n", " ", + RowBox[{"z2", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"992", "/", "27"}], " ", "+", " ", + RowBox[{"24", "*", "z3"}]}], ")"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"3778", "*", "z4"}], ")"}], "/", "27"}], " ", "-", + " ", + RowBox[{ + RowBox[{"(", + RowBox[{"304", "*", "z5"}], ")"}], "/", "9"}]}], ")"}]}]}], + ")"}], "*", + RowBox[{"Delta", "[", + RowBox[{"1", "-", "x"}], "]"}]}], ",", " ", "\n", " ", + RowBox[{"Delta", "[", + RowBox[{"1", "-", "x"}], "]"}], ",", " ", "1"}], "]"}], " ", "/.", + " ", "QCDConst"}]}], ";"}], "\n", + RowBox[{"(*", " ", + RowBox[{"Form", " ", "eq", " ", "4.7"}], " ", "*)"}], "\n", + RowBox[{ + RowBox[{"aggQ3PLU", " ", "=", " ", + RowBox[{ + RowBox[{"Coefficient", "[", " ", "\n", "\t\t", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"CA", "^", "2"}], "*", "TF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"32564", "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"32", "*", "B4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"3", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"3248", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"81", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"1796", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"104", "*", "z4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}], " ", + "+", " ", "\n", " ", + RowBox[{"CA", "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "35168"}], "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"560", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"1120", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "+", " ", + RowBox[{"NF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "55552"}], "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"160", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "+", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"448", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}]}], ")"}]}]}], ")"}]}], " ", "+", " ", "\n", + " ", + RowBox[{"CF", "*", "TF", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"6152", "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"64", "*", "B4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"3", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"40", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}], " ", "-", " ", + "\n", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"1208", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"9", "*", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"96", "*", "z4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}]}], + ")"}]}]}], " ", "//", "Simplify"}], "\n", " ", ",", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], "+", "x"}], ")"}], ",", + RowBox[{"-", "1"}]}], "]"}], " ", "/.", " ", "QCDConst"}]}], + ";"}]}]}]], "Code", + CellChangeTimes->{{3.948950055316721*^9, 3.948950063221066*^9}, { + 3.948950212826285*^9, 3.948950227872402*^9}, {3.948950356179121*^9, + 3.948950383652822*^9}, {3.948950501756506*^9, 3.948950536228887*^9}, { + 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, + 3.9489508160515337`*^9}, {3.948950869142365*^9, 3.948950905994871*^9}, { + 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, + 3.9489536787425423`*^9}}, + CellLabel-> + "In[271]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["12820", "27"]}], "+", + FractionBox[ + RowBox[{"2624", " ", "NF"}], "81"], "-", + FractionBox[ + RowBox[{"556", " ", "z2"}], "9"], "+", + FractionBox[ + RowBox[{"40", " ", "NF", " ", "z2"}], "9"], "-", + RowBox[{"24", " ", + SuperscriptBox["z2", "2"]}], "-", + FractionBox[ + RowBox[{"208", " ", "z3"}], "9"], "+", + FractionBox[ + RowBox[{"16", " ", "NF", " ", "z3"}], "9"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{ + FractionBox["1", "27"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "12337"}], "+", + RowBox[{"9", " ", "NF", " ", + RowBox[{"(", + RowBox[{"58", "+", + RowBox[{"17", " ", "z2"}]}], ")"}]}], "+", + RowBox[{"88", " ", "z3"}], "-", + RowBox[{"3", " ", "z2", " ", + RowBox[{"(", + RowBox[{"137", "+", + RowBox[{"128", " ", "ln2"}], "+", + RowBox[{"324", " ", "z3"}]}], ")"}]}]}], ")"}]}]}], "}"}]], "Output",\ + + CellChangeTimes->{{3.948950056566019*^9, 3.9489500690040627`*^9}, + 3.948950232810248*^9, {3.948950736657477*^9, 3.948950820817873*^9}, { + 3.9489508804035892`*^9, 3.948950910733629*^9}, {3.948951248372204*^9, + 3.9489512628739233`*^9}, 3.948953684019939*^9}, + CellLabel-> + "Out[271]=",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", + RowBox[{"Get", " ", "the", " ", "numerical", " ", "values"}], " ", "*)"}], + "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"qqNSasy", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], "\n", "\n", + RowBox[{"(*", " ", + RowBox[{ + RowBox[{ + RowBox[{"Here", " ", "we", " ", "have", " ", "that", " ", + RowBox[{"SExpansion", "[", " ", + RowBox[{ + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + RowBox[{"1", "/", + RowBox[{"(", + RowBox[{"1", "-", "x"}], ")"}]}], + RowBox[{"(", + RowBox[{ + RowBox[{"x", "^", + RowBox[{"(", + RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", + " ", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", + ",", "0"}], "]"}]}], " ", "\[Equal]", " ", + RowBox[{"-", " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ",", " ", + RowBox[{ + RowBox[{ + "so", " ", "we", " ", "add", " ", "the", " ", "piece", " ", "with", " ", + "a"}], " ", "-", " ", + RowBox[{"sign", "!"}]}]}], " ", "*)"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"ggasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "-", " ", + RowBox[{ + RowBox[{"(", + RowBox[{"aggQ3PLU", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}], + RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"ggasy", "[", + RowBox[{"[", "2", "]"}], "]"}], " ", "+", " ", + RowBox[{"(", + RowBox[{"aggQ3DEL", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], + " ", "//", " ", "Simplify"}]}]}]], "Code", + CellChangeTimes->{{3.948951282360952*^9, 3.948951363262577*^9}, { + 3.9489533926644917`*^9, 3.9489534137431717`*^9}, {3.94895350090244*^9, + 3.948953641550552*^9}}, + CellLabel-> + "In[274]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"20.36251906478134`", "\[VeryThinSpace]", "-", + RowBox[{"3.4050138869326796`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{ + RowBox[{"-", "72.36717694258661`"}], "+", + RowBox[{"3.11448410587291`", " ", "NF"}]}]}], "}"}]], "Output", + CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { + 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.948953688166637*^9}, + CellLabel-> + "Out[274]=",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1384.1265693540154`"}], "+", + RowBox[{"91.34702095227367`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]], "Output", + CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { + 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881680107`*^9}, + CellLabel-> + "Out[275]=",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], + +Cell[BoxData[ + RowBox[{"53.795479857509356`", "\[VeryThinSpace]", "+", + RowBox[{"11.129866602436904`", " ", "NF"}]}]], "Output", + CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { + 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881693697`*^9}, + CellLabel-> + "Out[276]=",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] +}, Open ]], + +Cell[BoxData[""], "Input", + CellChangeTimes->{{3.94895127781951*^9, + 3.9489512801199293`*^9}},ExpressionUUID->"783fabf2-705a-4b70-bf99-\ +6b0e4f5b0b1c"] +}, +WindowSize->{1920, 964}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, +FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) (June 19, 2020)", +StyleDefinitions->"Default.nb", +ExpressionUUID->"0a91d6a6-431d-4145-bf7f-17f592570909" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[558, 20, 197, 3, 30, "Input",ExpressionUUID->"b15860d2-997b-48de-9a18-81b5e0a2b6ce"], +Cell[CellGroupData[{ +Cell[780, 27, 758, 21, 110, "Code",ExpressionUUID->"cf4d06e7-cd27-4f38-a624-1bf2aace7b0c"], +Cell[CellGroupData[{ +Cell[1563, 52, 973, 26, 44, "Print",ExpressionUUID->"ee915aa4-2754-4223-bf26-787baf2d6893"], +Cell[2539, 80, 815, 22, 44, "Print",ExpressionUUID->"10592614-5c1d-48ee-b699-00d5f161866b"] +}, Open ]] +}, Open ]], +Cell[3381, 106, 1784, 47, 148, "Code",ExpressionUUID->"3e9423b7-e0d4-4093-b3ce-955024eadbb5"], +Cell[5168, 155, 485, 12, 94, "Input",ExpressionUUID->"38ac9fa3-fd03-4c80-97d5-f0a3587299c5"], +Cell[5656, 169, 1400, 37, 110, "Code",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], +Cell[CellGroupData[{ +Cell[7081, 210, 2840, 81, 148, "Code",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], +Cell[9924, 293, 393, 8, 34, "Output",ExpressionUUID->"932538e5-3fcc-4d6a-8839-992b3e2af928"], +Cell[10320, 303, 667, 18, 51, "Output",ExpressionUUID->"0ccc496d-ebd3-4707-91cd-5192d14850da"], +Cell[10990, 323, 389, 8, 51, "Output",ExpressionUUID->"580512ef-0d2c-49df-9693-7668a37ccce8"], +Cell[11382, 333, 269, 5, 24, "Print",ExpressionUUID->"c498f812-14d3-4a68-9da2-c8e933e5afc4"], +Cell[11654, 340, 1147, 34, 50, "Output",ExpressionUUID->"918f1b3f-684b-41b7-bb1e-09e8ac524de5"] +}, Open ]], +Cell[CellGroupData[{ +Cell[12838, 379, 818, 23, 72, "Code",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], +Cell[13659, 404, 202, 4, 34, "Output",ExpressionUUID->"d3bc2ff3-a6a1-4b6c-985e-9651a6d3b117"] +}, Open ]], +Cell[CellGroupData[{ +Cell[13898, 413, 749, 19, 72, "Code",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], +Cell[14650, 434, 2074, 56, 97, "Output",ExpressionUUID->"14f874a8-730a-4bee-bb0b-f93be4c938f2"] +}, Open ]], +Cell[CellGroupData[{ +Cell[16761, 495, 1019, 27, 110, "Code",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], +Cell[17783, 524, 2053, 55, 97, "Output",ExpressionUUID->"31a2b1bc-7efa-42df-bd24-d103791159cf"], +Cell[19839, 581, 300, 6, 34, "Output",ExpressionUUID->"c46fc0e1-a4fd-40d6-8949-8d1c6b684e2a"] +}, Open ]], +Cell[CellGroupData[{ +Cell[20176, 592, 12837, 332, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], +Cell[33016, 926, 1469, 42, 51, "Output",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] +}, Open ]], +Cell[CellGroupData[{ +Cell[34522, 973, 2350, 66, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], +Cell[36875, 1041, 590, 14, 34, "Output",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], +Cell[37468, 1057, 434, 10, 34, "Output",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], +Cell[37905, 1069, 357, 6, 34, "Output",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] +}, Open ]], +Cell[38277, 1078, 153, 3, 30, "Input",ExpressionUUID->"783fabf2-705a-4b70-bf99-6b0e4f5b0b1c"] +} +] +*) + diff --git a/extras/ome_n3lo/notebooks/Xspace.m b/extras/ome_n3lo/notebooks/Xspace.m new file mode 100644 index 000000000..7af32d1a1 --- /dev/null +++ b/extras/ome_n3lo/notebooks/Xspace.m @@ -0,0 +1,1423 @@ +(* + Xspace.m + +------------------------------------------------------------------------------------- + + "The Unpolarized and Polarized Single-Mass Three-Loop Heavy + Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$" + + Authors: J. Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, + A.~Goedicke, A.~von~Manteuffel, C.~Schneider, and K.~Sch\"onwald + + DESY 15-112 + + Any use of the code AGG requires to cite the above reference. + +------------------------------------------------------------------------------------- +------------------------------------------------------------------------------------- + + The x-space contributions to aggQ3 and \Delta aggQ3. + Delta and plus-contributions are identical in the unpolarized and polarized case. + + B4 = -4*z2*ln2^2+2/3*ln2^4-13/2*z4+16*li4fhalf + We use HarmonicSums notation. To interprete the expressions directly + one needs to use the mathematica package HarmonicSums. + +-------------------------------------------------------------------------------------*) + + + DEL = (CF*TF^2*(-1478/81 + NF*(-1942/81 - (20*z2)/3) - (88*z2)/3 - 7*z3) + + (64*TF^3*z3)/27 + CF^2*TF*(274/9 + (95*z3)/3) + + CA*(TF^2*(2587/135 + (572*z2)/27 + NF*(-178/9 + (196*z2)/27) - + (291*z3)/10) + CF*TF*(16541/162 - (64*B4)/3 + 52*z2 - (2617*z3)/12 + + (128*z4)/3)) + CA^2*TF*(34315/324 + (32*B4)/3 + (20435*z3)/216 + + z2*(992/27 + 24*z3) - (3778*z4)/27 - (304*z5)/9))*Delta[1-x]; + + PLU = CA^2*TF*(32564/(729*(-1 + x)) + (32*B4)/(3*(-1 + x)) + + (3248*z2)/(81*(-1 + x)) + (1796*z3)/(27*(-1 + x)) + (104*z4)/(1 - x)) + + CA*(TF^2*(-35168/(729*(-1 + x)) - (560*z2)/(27*(-1 + x)) - + (1120*z3)/(27*(-1 + x)) + NF*(-55552/(729*(-1 + x)) - + (160*z2)/(27*(-1 + x)) + (448*z3)/(27*(-1 + x)))) + + CF*TF*(6152/(27*(-1 + x)) - (64*B4)/(3*(-1 + x)) - (40*z2)/(1 - x) - + (1208*z3)/(9*(-1 + x)) - (96*z4)/(1 - x))); + + REGUNP = CF*TF^2*((-32*(587825 + 510903*x + 144333*x^2 + 466579*x^3 + 233280*x^4 + + 120960*x^5))/(127575*x) + (656*(1 + x)*z4)/9 - + (64*Sqrt[1 - x]*(-4853 - 134604*x - 15168*x^2 + 141920*x^3 + 26880*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(4725*x^(3/2)) - + (64*Sqrt[1 - x]*(-4853 - 134604*x - 15168*x^2 + 141920*x^3 + 26880*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(4725*x^(3/2)) + + (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(45*x) + + (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) - + (64*(-366907 + 520277*x - 325024*x^2 - 436536*x^3 + 200160*x^4 + + 60480*x^5)*H[0, x])/42525 - (32*(-1925 - 28952*x + 8590*x^2)*H[0, x]^2)/ + 14175 + (8*(635 + 821*x + 80*x^2)*H[0, x]^3)/405 + + (28*(1 + x)*H[0, x]^4)/27 + + z3*((16*(1220 + 3455*x + 821*x^2 + 180*x^3))/(135*x) - + (224*(1 + x)*H[0, x])/9) + + ((-64*(-1 + x)*(32375 + 241607*x - 500920*x^2 - 175896*x^3 + 260640*x^4 + + 60480*x^5))/(42525*x) - (64*(-1 + x)*(-32 + 85*x + 22*x^2)*H[0, x])/ + (81*x) + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + + ((-16*(-1 + x)*(-32 + 85*x + 22*x^2))/(81*x) - + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 - + (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + + ((-64*(-5600 + 50750*x - 9352*x^2 + 2815*x^3))/(14175*x) - + (64*(-4 - 5*x - 5*x^2 + 8*x^3)*H[0, x])/(27*x) - + (64*(1 + x)*H[0, x]^2)/9 + (64*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/ + (9*x))*H[0, 1, x] - (64*(1 + x)*H[0, 1, x]^2)/3 + + z2*((-16*(21525 - 239225*x + 54733*x^2 + 8515*x^3))/(14175*x) - + (8*(455 - 43*x + 440*x^2)*H[0, x])/135 + (232*(1 + x)*H[0, x]^2)/9 - + (176*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + + (352*(1 + x)*H[0, 1, x])/9) + + ((256*(-5 + 20*x + 11*x^2 + 25*x^3))/(135*x) + (512*(1 + x)*H[0, x])/9)* + H[0, 0, 1, x] + ((-64*(-20 - 16*x + 11*x^2 + 22*x^3))/(27*x) + + (128*(1 + x)*H[0, x])/9)*H[0, 1, 1, x] - (1280*(1 + x)*H[0, 0, 0, 1, x])/ + 9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + (64*(1 + x)*H[0, 1, 1, 1, x])/9 + + NF*((-64*(-1 + x)*(1825 + 11671*x + 4579*x^2))/(729*x) + + (208*(1 + x)*z4)/9 + (64*(2846 + 2675*x + 332*x^2)*H[0, x])/243 - + (32*(-109 - 55*x + 68*x^2)*H[0, x]^2)/81 - + (16*(-31 - 61*x + 8*x^2)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + + z3*((64*(-28 - 43*x - 4*x^2 + 18*x^3))/(27*x) - (640*(1 + x)*H[0, x])/ + 9) + ((128*(-1 + x)*(247 - 5*x + 166*x^2))/(243*x) - + (64*(-1 + x)*(14 + 113*x + 68*x^2)*H[0, x])/(81*x) - + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + + ((-16*(-1 + x)*(152 + 197*x + 206*x^2))/(81*x) + + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 + + (112*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + + ((-64*(14 + 271*x + 127*x^2 + 35*x^3))/(81*x) + + (128*(-2 + 11*x + 20*x^2 + 4*x^3)*H[0, x])/(27*x) + + (64*(1 + x)*H[0, x]^2)/9)*H[0, 1, x] + + z2*((16*(42 + 985*x + 553*x^2 + 208*x^3))/(81*x) - + (16*(25 + 37*x + 4*x^2)*H[0, x])/27 - (16*(1 + x)*H[0, x]^2)/9 - + (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + + (32*(1 + x)*H[0, 1, x])/9) + + ((-128*(-2 + 11*x + 20*x^2 + 4*x^3))/(27*x) - (128*(1 + x)*H[0, x])/9)* + H[0, 0, 1, x] + ((64*(4 + 50*x + 59*x^2 + 10*x^3))/(27*x) - + (128*(1 + x)*H[0, x])/9)*H[0, 1, 1, x] + + (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - + (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + + CA^2*TF*((32*B4*(-55 + 29*x + 3*x^2 + 5*x^3))/(15*x) + + (2*(136080 + 10390850*x - 25228915*x^2 + 41091867*x^3 - 35285580*x^4 - + 2505916*x^5 + 16253784*x^6 - 4708800*x^7 + 103680*x^8))/ + (18225*(-1 + x)*x^2) - (1184*(1 + 3*x)*z5)/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - + 468834*x^5 + 147720*x^6 - 2880*x^7 - 3600*Sqrt[1 - x]*x^(3/2)* + Sqrt[-((-1 + x)*x)] + 7200*Sqrt[1 - x]*x^(5/2)*Sqrt[-((-1 + x)*x)]))/ + (675*(-((-1 + x)*x))^(3/2)) - 3072*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + x]) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ + (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ + (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/ + (15*x) + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((2*(-15120 + 329300*x + 1049115*x^2 - 2509187*x^3 + 2443924*x^4 + + 2516114*x^5 - 8557392*x^6 + 6400296*x^7 - 1719360*x^8 + 34560*x^9))/ + (2025*(-1 + x)*x^2) + (4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - + 52837*x^4 - 3100*x^5 + 38183*x^6)*H[-1, x])/ + (405*(-1 + x)*x^2*(1 + x)) - + (8*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7)*H[-1, x]^2)/(45*(-1 + x)^2*x^3) + + (16*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x]^3)/(27*x*(1 + x)))* + H[0, x] + ((-15120 - 225360*x + 502300*x^2 + 601385*x^3 - 1157959*x^4 - + 327521*x^5 + 757679*x^6 - 119204*x^7)/(2025*(-1 + x)^2*x^2*(1 + x)) - + (4*(-378 - 2874*x + 6011*x^2 - 475*x^3 - 4369*x^4 + 4433*x^5 - + 1324*x^6 + 56*x^7)*H[-1, x])/(135*(-1 + x)^2*x^3) + + (4*(10 + 146*x + 267*x^2 + 143*x^3 + 4*x^4)*H[-1, x]^2)/(9*x*(1 + x)))* + H[0, x]^2 + ((-8*(72 + 269*x + 97*x^2 + 110*x^3))/(81*x) - + (8*(-12 - 18*x - 19*x^2 - 24*x^3 + 5*x^4 + 12*x^5)*H[-1, x])/ + (27*x^2*(1 + x)))*H[0, x]^3 - (2*(-20 + 41*x + 20*x^2 - 41*x^3 + 4*x^4)* + H[0, x]^4)/(27*(-1 + x)*(1 + x)) - (4*x*H[0, x]^5)/15 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* + ((-256*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 1536*(1 + x)*H[0, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* + ((-256*(180 - 167*x + 73*x^2 + 20*x^3))/(15*x) + 1536*(1 + x)*H[0, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - + 468834*x^5 + 147720*x^6 - 2880*x^7 - 3600*Sqrt[1 - x]*x^(3/2)* + Sqrt[-((-1 + x)*x)] + 7200*Sqrt[1 - x]*x^(5/2)*Sqrt[-((-1 + x)*x)]))/ + (675*(-((-1 + x)*x))^(3/2)) - 3072*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((-512*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 3072*(1 + x)*H[0, x])) + + ((2*(-45360 - 75530*x + 1565645*x^2 - 4951401*x^3 + 3302942*x^4 + + 11660542*x^5 - 25672176*x^6 + 19200888*x^7 - 5158080*x^8 + + 103680*x^9))/(6075*(-1 + x)*x^2) + + ((-2*(22014 - 8237*x - 114683*x^2 + 225135*x^3 - 153683*x^4 + + 42334*x^5))/(405*(-1 + x)*x^2) + + (16*(-1 + x)*(-42 + 328*x + 267*x^2 + 294*x^3 + 122*x^4)*H[-1, x])/ + (45*x^3))*H[0, x] - (2*(252 - 2700*x - 4114*x^2 + 6895*x^3 + + 10437*x^4 - 6242*x^5 - 10300*x^6 - 3201*x^7 + 3725*x^8 + 2368*x^9)* + H[0, x]^2)/(135*(-1 + x)^2*x^3*(1 + x)^2) - + (4*(24 + 4*x + 69*x^2 - 162*x^3 + 21*x^4 + 64*x^5)*H[0, x]^3)/ + (27*(-1 + x)*x^2))*H[1, x] + + ((-1536 + 3326*x - 1155*x^2 + 411*x^3 - 248*x^4)/(81*x^2) - + (2*(48 + 482*x + 601*x^2 - 199*x^3 - 863*x^4 - 127*x^5 + 82*x^6)* + H[0, x])/(27*x^2*(1 + x)^2) + + (2*(24 + 4*x + 29*x^2 - 93*x^3 + 58*x^4 + 30*x^5)*H[0, x]^2)/ + (9*(-1 + x)*x^2))*H[1, x]^2 - (4*(16 - 31*x + 45*x^2 - 32*x^3 + 18*x^4)* + H[0, x]*H[1, x]^3)/(27*(-1 + x)*x) + + z4*((-2*(27640 - 13006*x - 80398*x^2 + 35703*x^3 + 75319*x^4 - 25548*x^5 - + 20424*x^6 + 4111*x^7 - 2377*x^8 + 2340*x^9))/ + (45*(-1 + x)^3*x*(1 + x)^3) + 32*(1 + x)*H[-1, x] - + (4*(69 + 113*x)*H[0, x])/3 + 28*(-1 + x)*H[1, x]) - + (32*(-370 - 27*x^2 + 122*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((-4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - 52837*x^4 - 3100*x^5 + + 38183*x^6))/(405*(-1 + x)*x^2*(1 + x)) + + (16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - + (16*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + ((8*(-378 - 2772*x + 3157*x^2 - 3904*x^3 + 9996*x^4 + 4058*x^5 - + 11795*x^6 + 4238*x^7 + 280*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - + (16*(12 + 44*x + 163*x^2 + 149*x^3 + 12*x^4)*H[-1, x])/(9*x^2))* + H[0, x] + (4*(120 + 1880*x - 3389*x^2 + 722*x^3 - 248*x^4 + 362*x^5 + + 3917*x^6 - 2804*x^7 + 160*x^8)*H[0, x]^2)/(45*(-1 + x)^3*x^2* + (1 + x)) - (16*(-1 + x)*H[0, x]^3)/3 + + ((-16*(-1 + x)*(-42 + 328*x + 267*x^2 + 294*x^3 + 122*x^4))/(45*x^3) + + (32*(22 - 51*x^2 + 19*x^3 + 14*x^4)*H[0, x])/(9*(-1 + x)*x) - + 48*(-1 + x)*H[0, x]^2)*H[1, x])*H[0, -1, x] + + ((16*(6 + 95*x - 189*x^2 + 24*x^3 + 84*x^4 - 25*x^5 + 105*x^6 - 86*x^7 + + 10*x^8))/(9*(-1 + x)^3*x^2*(1 + x)) + (128*(-1 + x)*H[0, x])/3 - + 32*(-1 + x)*H[1, x])*H[0, -1, x]^2 + + ((-2*(125190 - 366745*x - 327315*x^2 + 1460740*x^3 - 437031*x^4 - + 1182779*x^5 + 637806*x^6 + 44234*x^7))/(2025*(-1 + x)^2*x^2* + (1 + x)) + (16*(1 + x)*(-42 - 318*x + 277*x^2 + 146*x^3 + 52*x^4)* + H[-1, x])/(45*x^3) + (16*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x]^2)/(3*x) + + ((4*(252 - 3432*x + 1198*x^2 + 11292*x^3 - 11065*x^4 - 5263*x^5 + + 4433*x^6 - 5117*x^7 + 3382*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - + (16*(-12 - 26*x - 75*x^2 - 60*x^3 + 4*x^4)*H[-1, x])/(9*x^2))* + H[0, x] + ((4*(24 - 184*x - 101*x^2 + 224*x^3 + 67*x^4 + 446*x^5 - + 57*x^6 - 828*x^7 - 235*x^8 + 342*x^9 + 110*x^10))/ + (9*(-1 + x)^3*x^2*(1 + x)^3) + 16*(1 + x)*H[-1, x])*H[0, x]^2 + + (40*(1 + x)*H[0, x]^3)/3 + + ((-4*(504 - 3456*x + 3508*x^2 + 13669*x^3 - 7102*x^4 - 17810*x^5 + + 4874*x^6 + 7057*x^7 + 556*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) - + (8*(24 + 28*x + 146*x^2 - 363*x^3 + 159*x^4 + 62*x^5)*H[0, x])/ + (9*(-1 + x)*x^2) + 16*(-1 + x)*H[0, x]^2)*H[1, x] - + (4*(20 + 60*x - 189*x^2 + 87*x^3 + 14*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + + ((16*(-380 + 558*x - 885*x^2 + 607*x^3 + 140*x^4))/(45*(-1 + x)*x) - + (64*(-1 + 11*x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + + ((8*(120 + 380*x - 553*x^2 - 1859*x^3 - 246*x^4 + 1516*x^5 + 1229*x^6 + + 363*x^7 + 90*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) - + 32*(1 + x)*H[-1, x] + (8*(5 + 41*x)*H[0, x])/3)*H[0, 1, x]^2 + + z3*((2*(-40222 + 34737*x + 214994*x^2 - 69552*x^3 - 305462*x^4 + + 27593*x^5 + 129250*x^6 + 22*x^7))/(135*(-1 + x)^2*x*(1 + x)^2) + + (8*(-480 - 120*x + 898*x^2 + 135*x^3 + 261*x^4 + 1930*x^5 - 876*x^6 - + 1085*x^7 + 437*x^8 + 340*x^9)*H[0, x])/(45*(-1 + x)^3*x*(1 + x)^3) + + 112*x*H[0, x]^2 + H[-1, x]* + ((8*(12 + 58*x + 257*x^2 + 393*x^3 + 210*x^4 + 12*x^5))/ + (9*x^2*(1 + x)) - 32*(1 + x)*H[0, x]) + + ((8*(48 - 48*x + 41*x^2 + 18*x^3 - 83*x^4 + 44*x^5))/(9*(-1 + x)*x^2) - + 48*(-1 + x)*H[0, x])*H[1, x] - (16*(-17 + 5*x)*H[0, -1, x])/3 + + (32*(-8 + x)*H[0, 1, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x]* + ((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + + 96*x^6))/(45*(-1 + x)*x^3) + (512*(180 - 167*x + 73*x^2 + 20*x^3)* + H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + + (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - + 3072*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + x]*((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + + 96*x^6))/(45*(-1 + x)*x^3) + (512*(180 - 167*x + 73*x^2 + 20*x^3)* + H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + + (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - + 3072*(1 + x)*H[0, 1, x]) + + ((-16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7))/(45*(-1 + x)^2*x^3) + + (32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x])/(9*x*(1 + x)) - + (16*(24 + 210*x - 303*x^2 - 105*x^3 - 42*x^4 + 208*x^5 + 345*x^6 - + 297*x^7 + 8*x^8)*H[0, x])/(9*(-1 + x)^3*x^2*(1 + x)) - + 48*(-1 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, x]*H[1, x] - + (256*(-1 + x)*H[0, -1, x])/3 - 64*(-1 + x)*H[0, 1, x])*H[0, -1, -1, x] + + ((16*(42 - 380*x + 41*x^2 - 477*x^3 - 198*x^4 + 192*x^5))/(45*x^3) - + (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - + (16*(-60 - 450*x + 397*x^2 - 894*x^3 + 927*x^4 + 120*x^5)*H[0, x])/ + (45*(-1 + x)*x^2) + 32*(-2 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, -1, x])* + H[0, -1, 1, x] + + ((-8*(-378 - 2292*x + 3177*x^2 - 13344*x^3 + 24836*x^4 + 8052*x^5 - + 26699*x^6 + 9744*x^7 + 504*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) + + (16*(24 + 102*x + 268*x^2 + 357*x^3 + 179*x^4 + 20*x^5)*H[-1, x])/ + (9*x^2*(1 + x)) + (16*(-60 - 1970*x + 3421*x^2 - 876*x^3 + 83*x^4 + + 377*x^5 - 4344*x^6 + 2409*x^7 + 120*x^8)*H[0, x])/ + (45*(-1 + x)^3*x^2*(1 + x)) + (80*(-2 + 5*x)*H[0, x]^2)/3 + + ((-64*(22 - 51*x^2 + 19*x^3 + 14*x^4))/(9*(-1 + x)*x) + + 224*(-1 + x)*H[0, x])*H[1, x] - (224*(-1 + x)*H[0, -1, x])/3 + + (160*(1 + 7*x)*H[0, 1, x])/3)*H[0, 0, -1, x] + + ((-4*(252 - 3660*x + 1086*x^2 + 23085*x^3 - 15078*x^4 - 37064*x^5 + + 11230*x^6 + 9173*x^7 - 7570*x^8 + 4146*x^9))/ + (135*(-1 + x)^2*x^3*(1 + x)^2) - + (16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4)*H[-1, x])/(9*x^2) + + ((-8*(120 - 1980*x - 1639*x^2 + 2720*x^3 + 3217*x^4 + 2980*x^5 - + 4117*x^6 - 8720*x^7 - 861*x^8 + 3560*x^9 + 880*x^10))/ + (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x])*H[0, x] - + (16*(23 + 21*x)*H[0, x]^2)/3 + + ((16*(-12 + 66*x + 56*x^2 - 213*x^3 + 85*x^4 + 26*x^5))/ + (9*(-1 + x)*x^2) - 128*(-1 + x)*H[0, x])*H[1, x] + + (32*(-5 + 17*x)*H[0, -1, x])/3 - (64*(2 + 17*x)*H[0, 1, x])/3)* + H[0, 0, 1, x] + ((-16*(1 + x)*(-42 - 318*x + 277*x^2 + 146*x^3 + 52*x^4))/ + (45*x^3) - (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - + (16*(-60 - 450*x + 313*x^2 - 810*x^3 + 927*x^4 + 120*x^5)*H[0, x])/ + (45*(-1 + x)*x^2) + 32*(-2 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, -1, x] + + 64*(1 + x)*H[0, 1, x])*H[0, 1, -1, x] + + ((8*(504 - 3576*x + 2523*x^2 + 12509*x^3 - 6137*x^4 - 15000*x^5 + + 4229*x^6 + 6247*x^7 + 501*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) + + (128*(1 + x)^3*H[-1, x])/(9*x) + + ((8*(24 + 152*x + 640*x^2 + 517*x^3 - 872*x^4 - 902*x^5 + 248*x^6 + + 433*x^7 + 64*x^8))/(9*(-1 + x)*x^2*(1 + x)^3) + + 64*(1 + x)*H[-1, x])*H[0, x] - (64*(-1 + 2*x)*H[0, x]^2)/3 + + (16*(-4 + 16*x - 2*x^2 - 31*x^3 + 15*x^4 + 4*x^5)*H[1, x])/ + (3*(-1 + x)*x^2) + (176*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + + z2*((2*(15120 + 75320*x + 61440*x^2 - 157300*x^3 + 100449*x^4 - + 169674*x^5 - 289559*x^6 + 318304*x^7))/(2025*(-1 + x)^2*x^2* + (1 + x)) - (16*(4 + x)*z3)/3 + + (16*(-42 - 341*x + 850*x^2 - 715*x^3 - 117*x^4 + 1086*x^5 - 721*x^6 + + 60*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - + (8*(24 + 119*x + 183*x^2 + 118*x^3 + 22*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + ((-4*(-488 - 718*x - 1075*x^2 + 1830*x^3 + 3714*x^4 - 1714*x^5 - + 2151*x^6 + 314*x^7))/(27*(-1 + x)^2*x*(1 + x)^2) + + (8*(-12 + 46*x + 137*x^2 + 165*x^3 + 142*x^4 + 68*x^5)*H[-1, x])/ + (9*x^2*(1 + x)))*H[0, x] + + ((-4*(15 - 68*x - 75*x^2 + 202*x^3 + 243*x^4 - 200*x^5 - 105*x^6 + + 66*x^7 + 18*x^8))/(9*(-1 + x)^3*(1 + x)^3) + 8*(1 + x)*H[-1, x])* + H[0, x]^2 + 8*(1 + x)*H[0, x]^3 + + ((8*(130 + 1261*x + 1069*x^2 - 2361*x^3 - 2613*x^4 + 1229*x^5 + + 1444*x^6 + 141*x^7))/(45*(-1 + x)*x^2*(1 + x)^2) + + (16*(30 - 47*x + 118*x^2 - 195*x^3 + 85*x^4 + 25*x^5)*H[0, x])/ + (9*(-1 + x)*x^2) + 8*(-1 + x)*H[0, x]^2)*H[1, x] + + (4*(12 + 19*x - 90*x^2 + 47*x^3 + 4*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + + ((-8*(60 + 1090*x - 2702*x^2 + 2241*x^3 - 634*x^4 - 1834*x^5 + + 3876*x^6 - 1977*x^7 + 120*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) + + (32*(-5 + 2*x)*H[0, x])/3 + 32*(-1 + x)*H[1, x])*H[0, -1, x] + + ((-8*(300 - 310*x - 1888*x^2 - 2639*x^3 - 2446*x^4 + 656*x^5 + + 4604*x^6 + 3053*x^7 + 430*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) + + 32*(1 + x)*H[-1, x] - (32*(5 + 8*x)*H[0, x])/3)*H[0, 1, x] + + (64*(-1 + x)*H[0, -1, -1, x])/3 - 64*x*H[0, -1, 1, x] - + (16*(-13 + 43*x)*H[0, 0, -1, x])/3 + (32*(12 + 17*x)*H[0, 0, 1, x])/3 - + 64*x*H[0, 1, -1, x] - (80*(1 + x)*H[0, 1, 1, x])/3) + + ((-32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4))/(9*x*(1 + x)) + + (256*(-1 + x)*H[0, x])/3)*H[0, -1, -1, -1, x] + + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - 64*(-1 + x)*H[0, x])* + H[0, -1, -1, 1, x] + + ((-16*(60 + 440*x + 776*x^2 - 605*x^3 - 1066*x^4 + 225*x^5 + 250*x^6))/ + (45*(-1 + x)*x^2*(1 + x)) + (32*(3 + 17*x)*H[0, x])/3)* + H[0, -1, 0, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - + 64*(-1 + x)*H[0, x])*H[0, -1, 1, -1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, -1, 1, 1, x] + + ((-16*(24 + 102*x + 268*x^2 + 357*x^3 + 179*x^4 + 20*x^5))/ + (9*x^2*(1 + x)) - (64*(-5 + 8*x)*H[0, x])/3)*H[0, 0, -1, -1, x] + + ((16*(120 + 350*x + 927*x^2 + 945*x^3 + 50*x^4))/(45*x^2) + + (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + + ((-8*(-120 - 6000*x + 10349*x^2 - 3180*x^3 + 134*x^4 + 2788*x^5 - + 14283*x^6 + 6352*x^7 + 1080*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) - + (32*(1 + 64*x)*H[0, x])/3 - 384*(-1 + x)*H[1, x])*H[0, 0, 0, -1, x] + + ((8*(120 - 3040*x - 3262*x^2 + 3305*x^3 + 7136*x^4 + 5735*x^5 - 8426*x^6 - + 17625*x^7 - 748*x^8 + 6825*x^9 + 1340*x^10))/ + (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x] + + 16*(35 + 27*x)*H[0, x] + 288*(-1 + x)*H[1, x])*H[0, 0, 0, 1, x] + + ((16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4))/(9*x^2) + + (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + + ((-16*(60 + 890*x - 236*x^2 - 2031*x^3 - 64*x^4 + 1271*x^5 + 290*x^6))/ + (45*(-1 + x)*x^2*(1 + x)) - (176*(5 + 3*x)*H[0, x])/3)* + H[0, 0, 1, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - + 64*(-1 + x)*H[0, x])*H[0, 1, -1, -1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, -1, 1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, 1, -1, x] + + ((-8*(-72 + 220*x - 201*x^2 - 12*x^3 + 25*x^4 + 20*x^5))/ + (9*(-1 + x)*x^2) + (32*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] + + (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 + + (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] + + (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + + (32*(-17 + 23*x)*H[0, 0, -1, 0, -1, x])/3 - + (32*(-9 + 55*x)*H[0, 0, -1, 0, 1, x])/3 + + 128*(1 + x)*H[0, 0, -1, 1, 1, x] + 32*(-17 + 23*x)*H[0, 0, 0, -1, -1, x] - + 32*(11 + 45*x)*H[0, 0, 0, -1, 1, x] + + (64*(26 + 59*x)*H[0, 0, 0, 0, -1, x])/3 - + (16*(213 + 137*x)*H[0, 0, 0, 0, 1, x])/3 - + 32*(11 + 45*x)*H[0, 0, 0, 1, -1, x] + 80*(11 + 21*x)*H[0, 0, 0, 1, 1, x] - + (64*(6 + 23*x)*H[0, 0, 1, 0, -1, x])/3 + + (32*(21 + 68*x)*H[0, 0, 1, 0, 1, x])/3 - + 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + + CF^2*TF*((64*B4*(-150 + 29*x + 38*x^2))/(15*x) - + (8*(5040 - 206320*x - 48375*x^2 + 145681*x^3 + 224786*x^4 - 242592*x^5 + + 56800*x^6))/(675*x^2) - (32*(5 + 137*x)*z5)/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((-512*Sqrt[1 - x]*(-1680 + 16064*x + 17227*x^2 - 47376*x^3 + 14640*x^4))/ + (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1)}, x] - 4096*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x]) + + (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(15*x) + + (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ + (15*x) + (4096*(-150 - 57*x + 38*x^2)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), (1 - VarGL)^(-1)}, x])/(15*x) + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 12288*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((-4*(-10080 + 78560*x + 401475*x^2 - 895353*x^3 - 673372*x^4 + + 2713024*x^5 - 1984224*x^6 + 413760*x^7))/(675*x^2) - + (32*(1 + x)*(-3442 + 3169*x + 233*x^2)*H[-1, x])/(135*x^2) - + (16*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4)*H[-1, x]^2)/ + (45*x^3) + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^3)/(9*x))*H[0, x] + + ((4*(-5040 - 93360*x + 204810*x^2 + 1735*x^3 + 7512*x^4))/(675*x^2) + + (8*(1 + x)*(252 + 2208*x - 5236*x^2 + 675*x^3 + 164*x^4)*H[-1, x])/ + (45*x^3) - (160*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(9*x))*H[0, x]^2 + + ((-2*(41 + 553*x + 8*x^2))/27 - (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/ + (27*x))*H[0, x]^3 - (4*(-3 - 3*x + 4*x^2)*H[0, x]^4)/27 + + (2*(1 + x)*H[0, x]^5)/15 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* + (-3072*(-1 + x) + 2048*(1 + x)*H[0, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* + ((1024*(-300 - 69*x + 31*x^2))/(15*x) + 2048*(1 + x)*H[0, x]) + + z4*((4*(63880 - 6891*x - 273*x^2 + 4140*x^3))/(45*x) - + (16*(61 + 109*x)*H[0, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((-512*Sqrt[1 - x]*(-1680 + 16064*x + 17227*x^2 - 47376*x^3 + 14640*x^4))/ + (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1)}, x] + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + (-6144*(-1 + x) + 4096*(1 + x)*H[0, x])) + + ((-16*(-1 + x)*(2520 + 61125*x - 100200*x^2 + 117297*x^3 + 285640*x^4 - + 392616*x^5 + 103440*x^6))/(675*x^2) + + ((16*(-1 + x)*(-6380 + 7348*x + 9085*x^2 + 1260*x^3))/(135*x^2) + + (64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3)*H[-1, x])/(45*x^3))* + H[0, x] + (4*(-1 + x)*(168 - 1472*x - 3312*x^2 - 747*x^3 + 308*x^4)* + H[0, x]^2)/(45*x^3) - (16*(-1 + x)*(8 + 23*x + 8*x^2)*H[0, x]^3)/ + (27*x))*H[1, x] + ((-8*(-1 + x)*(-6 - 80*x + 89*x^2))/(9*x) + + (8*(-1 + x)*(-8 + 33*x + 16*x^2)*H[0, x])/(9*x) + 8*(-1 + x)*H[0, x]^2)* + H[1, x]^2 + ((-4*(-1 + x)*(-20 + 17*x + 52*x^2))/(27*x) - + (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^3 - + (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) - + (128*(-410 + 429*x^2)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((32*(1 + x)*(-3442 + 3169*x + 233*x^2))/(135*x^2) + + (32*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4)*H[-1, x])/ + (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(3*x) + + ((16*(-252 - 2460*x + 3028*x^2 + 5201*x^3 - 539*x^4 + 164*x^5))/ + (45*x^3) + (512*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] + + (16*(-2680 + 1062*x - 747*x^2 + 120*x^3)*H[0, x]^2)/(45*x) - + (64*(-1 + x)*H[0, x]^3)/9 + + ((-64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) + + (128*(-1 + x)*(1 + 4*x + x^2)*H[0, x])/(3*x))*H[1, x])*H[0, -1, x] + + ((32*(-182 + 48*x - 21*x^2 + 10*x^3))/(9*x) + (256*(-1 + x)*H[0, x])/3)* + H[0, -1, x]^2 + + ((-16*(34420 - 91980*x - 112215*x^2 + 67150*x^3 + 15519*x^4))/(675*x^2) - + (64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3)*H[-1, x])/(45*x^3) + + ((-16*(-84 + 820*x + 920*x^2 - 1680*x^3 + 3365*x^4 + 74*x^5))/(45*x^3) - + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x))*H[0, x] + + (16*(172 + 45*x + 54*x^2 + 8*x^3)*H[0, x]^2)/(9*x) + + (32*(1 + x)*H[0, x]^3)/3 + + ((16*(168 - 1640*x - 2368*x^2 + 5431*x^3 - 1511*x^4 + 40*x^5))/ + (45*x^3) + (32*(-1 + x)*(4 - 11*x + 4*x^2)*H[0, x])/(3*x))*H[1, x] + + (16*(-1 + x)*(4 - 11*x + 4*x^2)*H[1, x]^2)/(9*x) + + ((128*(145 + 71*x + 61*x^2 + 5*x^3))/(15*x) - 128*(1 + x)*H[0, x])* + H[0, -1, x])*H[0, 1, x] + + ((16*(-1860 + 3*x - 147*x^2 + 80*x^3))/(45*x) + 32*(1 + x)*H[0, x])* + H[0, 1, x]^2 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - + (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + + 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + x]*((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - + (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + + 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + + z3*((4*(-70004 + 3299*x - 4455*x^2 + 3368*x^3))/(45*x) - + (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/x + + (16*(390 - 663*x + 140*x^2)*H[0, x])/45 + (8*(-15 + x)*H[0, x]^2)/3 - + (16*(-1 + x)*(8 - 13*x + 8*x^2)*H[1, x])/(9*x) - + 192*(-1 + x)*H[0, -1, x] - (32*(1 + x)*H[0, 1, x])/3) + + ((-32*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4))/(45*x^3) + + (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - + (64*(-58 + 8*x - 15*x^2 + 6*x^3)*H[0, x])/(3*x) - + (320*(-1 + x)*H[0, x]^2)/3 - 256*(-1 + x)*H[0, -1, x])*H[0, -1, -1, x] + + ((64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) - + (256*(70 - 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, -1, 1, x] + + ((-16*(-252 - 2460*x + 3028*x^2 + 5841*x^3 - 239*x^4 + 492*x^5))/ + (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - + (64*(-2690 + 1338*x - 717*x^2 + 70*x^3)*H[0, x])/(45*x) + + (256*(-2 + 3*x)*H[0, x]^2)/3 - (256*(-1 + x)*(1 + 4*x + x^2)*H[1, x])/ + (3*x) - 128*(-1 + x)*H[0, -1, x] + 256*(1 + x)*H[0, 1, x])* + H[0, 0, -1, x] + + ((8*(-168 + 1640*x + 1840*x^2 - 4215*x^3 + 16165*x^4 + 228*x^5))/ + (45*x^3) + (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) + + (32*(-1760 - 507*x - 90*x^2 + 80*x^3)*H[0, x])/(45*x) - + (16*(23 + 31*x)*H[0, x]^2)/3 - (32*(-1 + x)*(8 - 25*x + 8*x^2)*H[1, x])/ + (3*x) + 256*(-1 + x)*H[0, -1, x] - (448*(1 + x)*H[0, 1, x])/3)* + H[0, 0, 1, x] + ((64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3))/(45*x^3) - + (256*(70 + 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, 1, -1, x] + + ((-32*(168 - 1640*x - 2348*x^2 + 5381*x^3 - 1551*x^4 + 145*x^5))/ + (45*x^3) - (128*(-6 + 24*x - 12*x^2 + 7*x^3)*H[0, x])/(9*x) - + (32*(1 + x)*H[0, x]^2)/3 - (32*(-1 + x)*(4 - 47*x + 4*x^2)*H[1, x])/ + (9*x) + (64*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + + z2*((4*(3360 - 31980*x - 136015*x^2 + 34035*x^3 + 14992*x^4))/(225*x^2) - + 16*(5 + 13*x)*z3 - (16*(1 + x)*(168 + 1472*x - 3486*x^2 + 453*x^3 + + 164*x^4)*H[-1, x])/(45*x^3) + (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/ + (3*x) + ((-2*(61 + 437*x + 144*x^2))/3 + + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] - + (8*(-1 + 25*x + 4*x^2)*H[0, x]^2)/3 + (4*(1 + x)*H[0, x]^3)/9 + + ((-4*(-1316 + 8217*x - 8157*x^2 + 1736*x^3))/(45*x) - + (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(9*x))*H[1, x] - + (4*(-1 + x)*(20 + 23*x + 20*x^2)*H[1, x]^2)/(3*x) + + ((-32*(-1780 + 666*x - 471*x^2 + 80*x^3))/(45*x) + + (128*(-1 + x)*H[0, x])/3)*H[0, -1, x] + + ((-8*(40 + 1611*x + 1041*x^2 + 260*x^3))/(45*x) + 32*(1 + x)*H[0, x])* + H[0, 1, x] + 128*(-1 + x)*H[0, -1, -1, x] - + 128*(-2 + 3*x)*H[0, 0, -1, x] + (32*(1 + 13*x)*H[0, 0, 1, x])/3 + + (176*(1 + x)*H[0, 1, 1, x])/3) + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + + 256*(-1 + x)*H[0, x])*H[0, -1, -1, -1, x] + + ((-256*(71 + 5*x^2))/15 + 256*H[0, x])*H[0, -1, 0, 1, x] + + ((128*(1 + x)*(1 - 4*x + x^2))/(3*x) - 256*(-1 + x)*H[0, x])* + H[0, 0, -1, -1, x] + ((-256*(5 + 157*x - 15*x^2 + 5*x^3))/(15*x) + + 256*(1 + 2*x)*H[0, x])*H[0, 0, -1, 1, x] + + ((32*(-8080 + 4782*x - 2121*x^2 + 80*x^3))/(45*x) - + 128*(-5 + 11*x)*H[0, x])*H[0, 0, 0, -1, x] + + ((-32*(-2660 - 786*x + 255*x^2 + 320*x^3))/(45*x) + 256*(2 + 3*x)*H[0, x])* + H[0, 0, 0, 1, x] + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + + 256*(1 + 2*x)*H[0, x])*H[0, 0, 1, -1, x] + + ((32*(1160 + 353*x - 37*x^2 + 40*x^3))/(15*x) - (256*(1 + x)*H[0, x])/3)* + H[0, 0, 1, 1, x] + ((16*(-8 + 165*x - 159*x^2 + 4*x^3))/(9*x) + + 64*(1 + x)*H[0, x])*H[0, 1, 1, 1, x] + + 512*(-1 + x)*H[0, -1, 0, -1, -1, x] + 1024*(-1 + x)* + H[0, 0, -1, -1, -1, x] + 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - + 768*x*H[0, 0, -1, 0, 1, x] + 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - + 2304*x*H[0, 0, 0, -1, 1, x] + (2048*(-1 + 4*x)*H[0, 0, 0, 0, -1, x])/3 - + (128*(19 + 31*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*x*H[0, 0, 0, 1, -1, x] + + (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*x*H[0, 0, 1, 0, -1, x] + + 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + + CA*(TF^2*((16*(245035 - 45308*x + 197365*x^2 - 167815*x^3 - 120420*x^4 + + 24192*x^5))/(25515*x) - (16*(-350 + 1353*x + 114*x^2 + 350*x^3)*z3)/ + (135*x) + (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - + 19744*x^5 + 21504*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(945*(-((-1 + x)*x))^(3/2)) + + (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - 19744*x^5 + + 21504*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ + (945*(-((-1 + x)*x))^(3/2)) - (512*(-6 + 83*x + 32*x^2)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(45*x) - + (512*(-6 + 83*x + 32*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) + + (8*(-774 - 248268*x + 274039*x^2 - 11407*x^3 + 48672*x^4 - 117576*x^5 + + 48384*x^6)*H[0, x])/(8505*(-1 + x)) + + (4*(-11228 - 2121*x + 6939*x^2 + 4898*x^3)*H[0, x]^2)/(2835*(-1 + x)) + + (112*(1 + x)*H[0, x]^3)/81 + + ((8*(-28490 - 28416*x + 162417*x^2 - 31927*x^3 - 20520*x^4 - 69192*x^5 + + 48384*x^6))/(8505*x) - (8*(-655 + 789*x - 660*x^2 + 466*x^3)* + H[0, x])/(405*x) - (8*(1 - x + 4*x^2)*H[0, x]^2)/(15*x))*H[1, x] - + (4*(-395 + 624*x - 225*x^2 + 206*x^3)*H[1, x]^2)/(405*x) + + z2*((-8*(16905 - 43918*x + 39984*x^2 - 38106*x^3 + 23623*x^4))/ + (2835*(-1 + x)*x) + (464*(1 + x)*H[0, x])/27 + + (16*(1 - x + 4*x^2)*H[1, x])/(15*x)) + + ((8*(4585 - 15806*x + 14847*x^2 - 15118*x^3 + 9980*x^4))/ + (2835*(-1 + x)*x) + (8*(18 + 133*x + 160*x^2)*H[0, x])/(135*x) - + (16*(1 - x + 4*x^2)*H[1, x])/(15*x))*H[0, 1, x] - + (16*(9 + 182*x + 164*x^2)*H[0, 0, 1, x])/(135*x) + + (8*(36 + 35*x + 152*x^2)*H[0, 1, 1, x])/(135*x) + + NF*((-8*(-13532 + 16627*x - 16271*x^2 + 20120*x^3))/(729*x) + + (64*(-7 + 18*x - 3*x^2 + 7*x^3)*z3)/(27*x) - + (8*(582 + 2127*x - 3607*x^2 + 1078*x^3)*H[0, x])/(243*(-1 + x)) - + (4*(-236 - 467*x + 52*x^2)*H[0, x]^2)/81 + (224*(1 + x)*H[0, x]^3)/ + 81 + z2*((-8*(-138 + 406*x + 175*x^2 + 190*x^3))/(81*x) - + (32*(1 + x)*H[0, x])/27) + + ((-8*(-358 + 111*x - 1263*x^2 + 1078*x^3))/(243*x) - + (8*(-52 + 33*x - 21*x^2 + 52*x^3)*H[0, x])/(81*x))*H[1, x] + + (4*(-52 + 33*x - 81*x^2 + 52*x^3)*H[1, x]^2)/(81*x) + + ((8*(-52 + 265*x + 268*x^2 + 104*x^3))/(81*x) + (128*(1 + x)*H[0, x])/ + 27)*H[0, 1, x] - (128*(1 + x)*H[0, 0, 1, x])/27 - + (128*(1 + x)*H[0, 1, 1, x])/27)) + + CF*TF*((-32*B4*(-260 + 87*x + 44*x^2 + 10*x^3))/(15*x) - + (4*(272160 - 9336320*x - 3300025*x^2 + 7190304*x^3 + 50470205*x^4 - + 62944172*x^5 + 24337368*x^6 - 6242400*x^7 + 103680*x^8))/ + (18225*(-1 + x)*x^2) + (16*(111 + 883*x)*z5)/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - + 258486*x^5 + 68760*x^6 - 960*x^7 - 1200*Sqrt[1 - x]*x^(3/2)* + Sqrt[-((-1 + x)*x)] + 2400*Sqrt[1 - x]*x^(5/2)* + Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1)}, x]) - + (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ + (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ + (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/ + (15*x) - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x] + 8192*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - + 16384*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 24576*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((-8*(-45360 + 356290*x - 844475*x^2 - 5885706*x^3 + 2623012*x^4 + + 15691737*x^5 - 23404896*x^6 + 14995908*x^7 - 3510000*x^8 + + 51840*x^9))/(6075*(-1 + x)*x^2) + + (8*(1 + x)*(-16197 + 7915*x + 167*x^2 + 4579*x^3)*H[-1, x])/ + (135*x^2) - (8*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4)* + H[-1, x]^2)/(45*x^3) - (32*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x]^3)/ + (27*x))*H[0, x] + + ((-4*(15120 + 245160*x - 1050320*x^2 + 300450*x^3 + 483824*x^4 + + 3741*x^5))/(2025*(-1 + x)*x^2) + + (4*(1 + x)*(-1512 - 13128*x + 23270*x^2 - 10781*x^3 + 4580*x^4)* + H[-1, x])/(135*x^3) - (8*(1 + x)*(28 + 101*x + 28*x^2)*H[-1, x]^2)/ + (9*x))*H[0, x]^2 + ((-4*(-288 + 2689*x - 4943*x^2 + 334*x^3))/ + (81*x) + (8*(1 + x)*(-8 + 12*x - 25*x^2 + 16*x^3)*H[-1, x])/(9*x^2))* + H[0, x]^3 + (4*(-74 + 91*x)*H[0, x]^4)/27 + (4*(-5 + 9*x)*H[0, x]^5)/ + 15 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* + ((1024*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 4096*(1 + x)*H[0, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* + ((1024*(240 - 49*x + 21*x^2 + 10*x^3))/(15*x) - 4096*(1 + x)*H[0, x]) + + z4*((4*(-53780 + 9019*x + 10387*x^2 + 1000*x^3))/(45*x) + + (8*(19 + 550*x)*H[0, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - + 258486*x^5 + 68760*x^6 - 960*x^7 - 1200*Sqrt[1 - x]*x^(3/2)* + Sqrt[-((-1 + x)*x)] + 2400*Sqrt[1 - x]*x^(5/2)* + Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((2048*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 8192*(1 + x)*H[0, x])) + + ((-8*(-15120 - 216235*x + 934785*x^2 - 2027062*x^3 + 906369*x^4 + + 4378379*x^5 - 7801632*x^6 + 4998636*x^7 - 1170000*x^8 + 17280*x^9))/ + (2025*(-1 + x)*x^2) + + ((-8*(8629 - 20936*x + 5657*x^2 - 11766*x^3 + 18596*x^4))/(135*x^2) - + (64*(-1 + x)*(-42 + 348*x + 571*x^2 + 370*x^3 + 61*x^4)*H[-1, x])/ + (45*x^3))*H[0, x] + (4*(504 - 5160*x - 8330*x^2 + 11955*x^3 - + 1125*x^4 + 1886*x^5)*H[0, x]^2)/(135*x^3) + + (8*(-1 + x)*(24 + 20*x + 137*x^2 + 32*x^3)*H[0, x]^3)/(27*x^2))* + H[1, x] + ((4*(-1 + x)*(-768 + 316*x - 590*x^2 + 1579*x^3))/(81*x^2) - + (16*(-4 - 30*x - 73*x^2 + 62*x^3 + 48*x^4)*H[0, x])/(9*x^2) - + (4*(-1 + x)*(24 + 28*x + 181*x^2 + 40*x^3)*H[0, x]^2)/(9*x^2))* + H[1, x]^2 + ((4*(-1 + x)*(10 + 127*x + 172*x^2))/(81*x) - + (16*(-1 + x)*(10 + 13*x + 10*x^2)*H[0, x])/(27*x))*H[1, x]^3 + + (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) + + (128*(-390 + 201*x^2 + 61*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((-8*(1 + x)*(-16197 + 7915*x + 167*x^2 + 4579*x^3))/(135*x^2) + + (16*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4)*H[-1, x])/ + (45*x^3) + (32*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x]^2)/(9*x) + + ((-8*(-504 - 4560*x + 3714*x^2 + 1123*x^3 - 1647*x^4 + 2004*x^5))/ + (45*x^3) + (32*(1 + x)*(12 + 52*x + 83*x^2 + 46*x^3)*H[-1, x])/ + (9*x^2))*H[0, x] - (8*(-120 - 4700*x + 756*x^2 - 3441*x^3 + + 160*x^4)*H[0, x]^2)/(45*x^2) + (176*(-1 + x)*H[0, x]^3)/9 + + ((64*(-1 + x)*(-42 + 348*x + 571*x^2 + 370*x^3 + 61*x^4))/(45*x^3) - + (64*(-1 + x)*(17 + 50*x + 17*x^2)*H[0, x])/(9*x))*H[1, x])* + H[0, -1, x] + ((-16*(-12 - 396*x + 39*x^2 - 174*x^3 + 10*x^4))/ + (9*x^2) - (32*(-1 + x)*H[0, x])/3)*H[0, -1, x]^2 + + ((8*(144555 - 761190*x + 895205*x^2 - 207590*x^3 + 324424*x^4 - + 659503*x^5 + 269499*x^6))/(2025*(-1 + x)^2*x^2) - + (64*(1 + x)*(-42 - 343*x + 576*x^2 - 205*x^3 + 26*x^4)*H[-1, x])/ + (45*x^3) - (448*(1 + x)^3*H[-1, x]^2)/(9*x) + + ((-8*(-504 + 6144*x + 4010*x^2 - 26835*x^3 + 39390*x^4 - 22715*x^5 + + 870*x^6))/(135*(-1 + x)*x^3) - + (32*(1 + x)*(12 + 28*x + 29*x^2 + 22*x^3)*H[-1, x])/(9*x^2))* + H[0, x] - (8*(-24 + 380*x + 41*x^2 + 365*x^3 + 96*x^4)*H[0, x]^2)/ + (9*x^2) - (208*(1 + x)*H[0, x]^3)/9 + + ((16*(504 - 4944*x + 4094*x^2 + 11713*x^3 - 18429*x^4 + 6364*x^5 + + 518*x^6))/(135*(-1 + x)*x^3) + + (16*(-24 - 16*x - 297*x^2 + 273*x^3 + 52*x^4)*H[0, x])/(9*x^2))* + H[1, x] + (16*(-6 - 21*x + 19*x^2 + 6*x^3)*H[1, x]^2)/(3*x) + + ((-32*(1330 + 228*x + 1023*x^2 + 170*x^3))/(45*x) + + (832*(1 + x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + + ((-16*(-120 - 1150*x + 507*x^2 - 123*x^3 + 20*x^4))/(45*x^2) - + (560*(1 + x)*H[0, x])/3)*H[0, 1, x]^2 + + z3*((4*(-156468 + 196381*x + 79647*x^2 - 127206*x^3 + 9806*x^4))/ + (135*(-1 + x)*x) - (16*(1 + x)*(4 + 20*x + 53*x^2 + 18*x^3)*H[-1, x])/ + (3*x^2) + (16*(-340 - 805*x + 4397*x^2)*H[0, x])/(45*x) - + (16*(-5 + 34*x)*H[0, x]^2)/3 + (16*(16 - 34*x + 25*x^2 - 5*x^3 + + 10*x^4)*H[1, x])/(3*x^2) + (256*(-1 + x)*H[0, -1, x])/3 - + (128*(1 + x)*H[0, 1, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + + 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - + (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + + 4096*(1 + x)*H[0, x]^2 - (2048*(-2 - 15*x + 13*x^2 + 2*x^3)*H[1, x])/ + (3*x) + 8192*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + + 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - + (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + + 4096*(1 + x)*H[0, x]^2 - (2048*(-2 - 15*x + 13*x^2 + 2*x^3)*H[1, x])/ + (3*x) + 8192*(1 + x)*H[0, 1, x]) + + ((-16*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4))/(45*x^3) - + (64*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x])/(9*x) - + (32*(24 + 460*x + 96*x^2 + 303*x^3 + 36*x^4)*H[0, x])/(9*x^2) + + 64*(-1 + x)*H[0, x]^2 + (512*(-1 + x)*H[0, -1, x])/3)* + H[0, -1, -1, x] + ((-64*(42 - 395*x - 233*x^2 + 31*x^3 + 179*x^4 + + 96*x^5))/(45*x^3) + (896*(1 + x)^3*H[-1, x])/(9*x) + + (32*(60 + 1530*x - 603*x^2 + 1278*x^3 + 280*x^4)*H[0, x])/(45*x^2))* + H[0, -1, 1, x] + ((8*(-1512 - 12720*x + 12142*x^2 - 5751*x^3 - + 3681*x^4 + 7444*x^5))/(135*x^3) - + (32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3)*H[-1, x])/(9*x^2) - + (16*(120 + 9460*x - 1803*x^2 + 6747*x^3 + 520*x^4)*H[0, x])/(45*x^2) - + (64*(-10 + 19*x)*H[0, x]^2)/3 + (128*(-1 + x)*(17 + 50*x + 17*x^2)* + H[1, x])/(9*x) - (256*(-1 + x)*H[0, -1, x])/3 - + (1664*(1 + x)*H[0, 1, x])/3)*H[0, 0, -1, x] + + ((-8*(504 - 6624*x - 3410*x^2 + 41115*x^3 - 64470*x^4 + 30839*x^5 + + 1326*x^6))/(135*(-1 + x)*x^3) + + (64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3)*H[-1, x])/(3*x^2) + + (16*(-120 + 3780*x + 1006*x^2 + 4405*x^3 + 1040*x^4)*H[0, x])/ + (45*x^2) + (32*(28 + 23*x)*H[0, x]^2)/3 - + (16*(8 - 20*x - 91*x^2 + 87*x^3 + 8*x^4)*H[1, x])/(3*x^2) + + (1312*(1 + x)*H[0, 1, x])/3)*H[0, 0, 1, x] + + ((64*(1 + x)*(-42 - 343*x + 576*x^2 - 205*x^3 + 26*x^4))/(45*x^3) + + (896*(1 + x)^3*H[-1, x])/(9*x) + + (32*(60 + 1530*x + 513*x^2 + 1278*x^3 + 280*x^4)*H[0, x])/(45*x^2))* + H[0, 1, -1, x] + ((16*(-1008 + 10008*x - 7708*x^2 - 22171*x^3 + + 33393*x^4 - 12308*x^5 + 154*x^6))/(135*(-1 + x)*x^3) - + (256*(1 + x)^3*H[-1, x])/(9*x) - + (16*(-24 - 72*x - 563*x^2 + 301*x^3 + 60*x^4)*H[0, x])/(9*x^2) + + (272*(1 + x)*H[0, x]^2)/3 - (16*(24 - 88*x - 165*x^2 + 153*x^3 + + 52*x^4)*H[1, x])/(9*x^2) - 192*(1 + x)*H[0, 1, x])*H[0, 1, 1, x] + + z2*((8*(-15120 + 22650*x + 299575*x^2 - 677365*x^3 + 565421*x^4 - + 328352*x^5 + 127791*x^6))/(2025*(-1 + x)^2*x^2) + + (8*(17 + 19*x)*z3)/3 - (8*(1 + x)*(-336 - 3004*x + 5586*x^2 - + 3197*x^3 + 836*x^4)*H[-1, x])/(45*x^3) + + (16*(1 + x)*(26 + 85*x + 26*x^2)*H[-1, x]^2)/(9*x) + + ((-4*(1216 + 4949*x + 5675*x^2 + 422*x^3))/(27*x) - + (8*(1 + x)*(-1 + 4*x)*(8 + 8*x + 7*x^2)*H[-1, x])/(3*x^2))*H[0, x] + + (8*(-85 - 160*x + 12*x^2)*H[0, x]^2)/9 - (8*(41 + 23*x)*H[0, x]^3)/9 + + ((4*(-1560 - 8738*x - 2161*x^2 + 41058*x^3 - 30541*x^4 + 2662*x^5))/ + (135*(-1 + x)*x^2) - (8*(-1 + x)*(120 + 64*x + 553*x^2 + 124*x^3)* + H[0, x])/(9*x^2))*H[1, x] - (4*(-4 - 41*x + 33*x^2 + 4*x^3)* + H[1, x]^2)/(3*x) + ((8*(-120 - 6360*x + 2061*x^2 - 4611*x^3 + + 140*x^4))/(45*x^2) - (112*(-1 + x)*H[0, x])/3)*H[0, -1, x] + + ((8*(-600 + 1460*x + 4*x^2 + 3229*x^3 + 600*x^4))/(45*x^2) + + (688*(1 + x)*H[0, x])/3)*H[0, 1, x] - (256*(-1 + x)*H[0, -1, -1, x])/ + 3 + (32*(-19 + 55*x)*H[0, 0, -1, x])/3 - + (16*(91 + 115*x)*H[0, 0, 1, x])/3 + (208*(1 + x)*H[0, 1, 1, x])/3) + + ((64*(1 + x)*(2 - 29*x + 2*x^2))/(9*x) - (512*(-1 + x)*H[0, x])/3)* + H[0, -1, -1, -1, x] - (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + + ((32*(-20 - 160*x + 77*x^2 + 105*x^3 + 30*x^4))/(15*x^2) - + (832*(1 + x)*H[0, x])/3)*H[0, -1, 0, 1, x] - + (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + + ((32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3))/(9*x^2) + + (896*(-1 + x)*H[0, x])/3)*H[0, 0, -1, -1, x] + + ((-64*(20 + 85*x - 222*x^2 + 140*x^3 + 55*x^4))/(15*x^2) - + (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + + ((16*(40 + 4740*x - 982*x^2 + 3351*x^3 + 600*x^4))/(15*x^2) + + (32*(-43 + 195*x)*H[0, x])/3)*H[0, 0, 0, -1, x] + + ((-16*(-120 + 5660*x + 1468*x^2 + 7945*x^3 + 1900*x^4))/(45*x^2) - + (32*(133 + 79*x)*H[0, x])/3)*H[0, 0, 0, 1, x] + + ((-64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3))/(3*x^2) - + (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + + ((16*(-120 - 5620*x - 1072*x^2 + 893*x^3 + 200*x^4))/(45*x^2) + + (1280*(1 + x)*H[0, x])/3)*H[0, 0, 1, 1, x] - + (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + + ((16*(72 - 172*x - 125*x^2 + 97*x^3 + 64*x^4))/(9*x^2) + + (64*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] - + (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 - + (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - + (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + + (256*(5 + 8*x)*H[0, 0, -1, 0, 1, x])/3 - + 640*(-1 + x)*H[0, 0, 0, -1, -1, x] + 128*(13 + 19*x)* + H[0, 0, 0, -1, 1, x] - (256*(3 + 46*x)*H[0, 0, 0, 0, -1, x])/3 + + 128*(22 + 9*x)*H[0, 0, 0, 0, 1, x] + 128*(13 + 19*x)* + H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + + (128*(13 + 19*x)*H[0, 0, 1, 0, -1, x])/3 - + (2464*(1 + x)*H[0, 0, 1, 0, 1, x])/3 + 1120*(1 + x)* + H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3)); + + REGPOL = CF*TF^2*((256*(-43 - 263*x + 441*x^2 - 630*x^3 + 180*x^4))/1215 + + (656*(1 + x)*z4)/9 + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + + 960*x^4)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ + (135*x^(3/2)) + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + + 960*x^4)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ + (135*x^(3/2)) - (8192*(-2 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/9 - + (8192*(-2 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1)}, x])/9 + (8*(121 + 19*x)*H[0, x]^3)/81 + + (28*(1 + x)*H[0, x]^4)/27 + z3*((-16*(-175 + 11*x))/27 - + (224*(1 + x)*H[0, x])/9) - (416*(-1 + x)*H[1, x]^2)/27 - + (80*(-1 + x)*H[1, x]^3)/27 + (704*(-95 + 13*x)*H[0, 1, x])/405 - + (64*(1 + x)*H[0, 1, x]^2)/3 + + H[1, x]*((128*(-1 + x)*(137 + 375*x + 474*x^2 - 1080*x^3 + 360*x^4))/405 + + (320*(-1 + x)*H[0, 1, x])/3) + H[0, x]^2*((8*(1675 + 97*x))/405 + + (160*(-1 + x)*H[1, x])/9 - (64*(1 + x)*H[0, 1, x])/9) + + z2*((-8*(-9605 + 2389*x))/405 - (8*(-347 + 307*x)*H[0, x])/27 + + (232*(1 + x)*H[0, x]^2)/9 - (880*(-1 + x)*H[1, x])/9 + + (352*(1 + x)*H[0, 1, x])/9) + (128*(-37 + 35*x)*H[0, 0, 1, x])/27 - + (64*(-88 + 83*x)*H[0, 1, 1, x])/27 + + H[0, x]*((32*(8341 - 6071*x - 1188*x^2 + 18648*x^3 - 17280*x^4 + + 4320*x^5))/1215 - (1664*(-1 + x)*H[1, x])/27 - + (160*(-1 + x)*H[1, x]^2)/9 - (64*(-41 + 31*x)*H[0, 1, x])/27 + + (512*(1 + x)*H[0, 0, 1, x])/9 + (128*(1 + x)*H[0, 1, 1, x])/9) - + (1280*(1 + x)*H[0, 0, 0, 1, x])/9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + + (64*(1 + x)*H[0, 1, 1, 1, x])/9 + + NF*((-199040*(-1 + x))/243 + (208*(1 + x)*z4)/9 - + (16*(-97 + 41*x)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + + z3*((64*(-85 + 74*x))/27 - (640*(1 + x)*H[0, x])/9) + + (14848*(-1 + x)*H[1, x])/81 + (32*(-1 + x)*H[1, x]^2)/27 + + (560*(-1 + x)*H[1, x]^3)/27 - (256*(25 + 16*x)*H[0, 1, x])/81 + + z2*((16*(343 + 313*x))/81 - (16*(19 + 7*x)*H[0, x])/27 - + (16*(1 + x)*H[0, x]^2)/9 - (80*(-1 + x)*H[1, x])/9 + + (32*(1 + x)*H[0, 1, x])/9) + H[0, x]^2*((-16*(-419 + 19*x))/81 - + (160*(-1 + x)*H[1, x])/9 + (64*(1 + x)*H[0, 1, x])/9) - + (128*(2 + 11*x)*H[0, 0, 1, x])/27 + (64*(14 + 23*x)*H[0, 1, 1, x])/27 + + H[0, x]*((64*(1895 + 1133*x))/243 - (1216*(-1 + x)*H[1, x])/27 + + (160*(-1 + x)*H[1, x]^2)/9 + (128*(2 + 11*x)*H[0, 1, x])/27 - + (128*(1 + x)*H[0, 0, 1, x])/9 - (128*(1 + x)*H[0, 1, 1, x])/9) + + (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - + (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + + CA^2*TF*((32*B4*(1 + 9*x))/3 - + (2*(-9720 - 613369*x + 525603*x^2 + 216232*x^3 + 219780*x^4 - 558360*x^5 + + 209952*x^6))/(729*(-1 + x)*x) - (1184*(3 + x)*z5)/3 - + (256*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^ + 2)/3 - (256*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + x]^2)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((32*(160 + 283*x + 1105*x^2 - 3702*x^3 + 2112*x^4))/ + (9*Sqrt[-((-1 + x)*x)]) - (512*(-33 + 29*x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((32*(160 + 283*x + 1105*x^2 - 3702*x^3 + 2112*x^4))/ + (9*Sqrt[-((-1 + x)*x)]) - 3072*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + x]) + (128*(20 - 26*x + 43*x^2 - 429*x^3 + 376*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) + + (128*(20 - 26*x + 43*x^2 - 429*x^3 + 376*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x])/(3*(-1 + x)*x^2) + + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + (16*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[-1, x]^3*H[0, x])/ + (27*x*(1 + x)) + (2*(-17 + 20*x + 5*x^2 - 24*x^3 + 12*x^4)*H[0, x]^4)/ + (27*(-1 + x)*(1 + x)) - (4*H[0, x]^5)/15 + + z4*((2*(638 + 4250*x - 661*x^2 - 4145*x^3 + 12*x^4))/ + (9*(-1 + x)*(1 + x)) + 32*(1 + x)*H[-1, x] - (4*(113 + 69*x)*H[0, x])/ + 3 - 28*(-1 + x)*H[1, x]) - + (8*(-38 + 14*x + 147*x^2 - 46*x^3 - 141*x^4 + 4*x^5)*H[0, -1, x]^2)/ + (9*(-1 + x)*x*(1 + x)) + (8*(52 - 290*x - 65*x^2 + 290*x^3 + 55*x^4 + + 10*x^5)*H[0, 1, x]^2)/(9*(-1 + x)*x*(1 + x)) + + H[0, x]^3*((-4*(-520 + 559*x + 8*x^2))/81 - + (4*(44 + 149*x - 402*x^2 + 221*x^3 + 8*x^4)*H[1, x])/(27*(-1 + x)*x) + + (16*(-1 + x)*H[0, -1, x])/3 + (40*(1 + x)*H[0, 1, x])/3) + + z3*((-2*(28707 + 16050*x - 28071*x^2 - 14990*x^3 + 496*x^4))/ + (27*(-1 + x)*(1 + x)) + 112*H[0, x]^2 + + H[-1, x]*((8*(50 + 37*x - 33*x^2 + 36*x^4))/(9*x*(1 + x)) - + 32*(1 + x)*H[0, x]) - (8*(-68 - 21*x + 150*x^2 - 89*x^3 + 8*x^4)* + H[1, x])/(9*(-1 + x)*x) + + H[0, x]*((-8*(238 + 231*x - 319*x^2 - 284*x^3 + 84*x^4))/ + (9*(-1 + x)*(1 + x)) + 48*(-1 + x)*H[1, x]) + + (16*(-5 + 17*x)*H[0, -1, x])/3 - (32*(-1 + 8*x)*H[0, 1, x])/3) + + H[-1, x]^2*((4*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)*H[0, x])/ + (27*x^2) + (4*(22 - 18*x - 75*x^2 - 15*x^3 + 28*x^4)*H[0, x]^2)/ + (9*x*(1 + x)) - (16*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[0, -1, x])/ + (9*x*(1 + x)) + (16*(1 + x)*(14 + 43*x + 14*x^2)*H[0, 1, x])/(9*x)) + + H[1, x]^2*((-954 + 1645*x - 371*x^2 - 54*x^3)/(27*x) - + (4*(12 + 92*x - 237*x^2 + 119*x^3 + 6*x^4)*H[0, 1, x])/(9*(-1 + x)*x)) + + (8*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)*H[0, -1, -1, x])/(27*x^2) + + (8*(90 - 53*x - 48*x^2 - 525*x^3 + 136*x^4)*H[0, -1, 1, x])/(27*x^2) + + (4*(-270 + 299*x + 1706*x^2 - 5120*x^3 - 1100*x^4 + 5357*x^5 + 56*x^6)* + H[0, 0, -1, x])/(27*(-1 + x)*x^2*(1 + x)) + + (4*(90 - 747*x - 807*x^2 + 3030*x^3 - 327*x^4 - 2839*x^5 + 632*x^6)* + H[0, 0, 1, x])/(27*(-1 + x)*x^2*(1 + x)) + + (8*(1 + x)*(90 + 127*x - 175*x^2 + 136*x^3)*H[0, 1, -1, x])/(27*x^2) + + H[0, -1, x]*((-16*(927 + 5978*x + 8862*x^2 + 4340*x^3 + 81*x^4))/ + (81*x*(1 + x)) + (32*(85 - 168*x + 83*x^2 + 4*x^3)*H[0, 1, x])/ + (9*(-1 + x)) + (256*(-1 + x)*H[0, -1, -1, x])/3 - + 64*(-1 + x)*H[0, -1, 1, x] + (224*(-1 + x)*H[0, 0, -1, x])/3 - + (32*(-17 + 5*x)*H[0, 0, 1, x])/3 - 64*(-1 + x)*H[0, 1, -1, x]) - + (8*(-180 + 72*x - 2401*x^2 + 5355*x^3 - 3044*x^4 + 108*x^5)*H[0, 1, 1, x])/ + (27*(-1 + x)*x^2) + H[0, x]^2* + ((-1080 + 9828*x - 21167*x^2 + 2231*x^3 + 25777*x^4 - 16183*x^5 - + 486*x^6)/(81*(-1 + x)^2*x*(1 + x)) - 1536*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x] - 1536*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] + (2*(52 + 5*x - 93*x^2 + 58*x^3 + 30*x^4)*H[1, x]^2)/ + (9*(-1 + x)*x) - (4*(-52 + 237*x + 267*x^2 - 341*x^3 - 283*x^4 + + 56*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + (4*(44 + 41*x - 481*x^2 - 65*x^3 + 431*x^4 + 38*x^5)*H[0, 1, x])/ + (9*(-1 + x)*x*(1 + x)) + H[1, x]* + ((-2*(-90 + 405*x + 850*x^2 - 2229*x^3 + 1144*x^4 + 72*x^5))/ + (27*(-1 + x)*x^2) + 48*(-1 + x)*H[0, -1, x] - + 16*(-1 + x)*H[0, 1, x]) + 48*(-1 + x)*H[0, -1, -1, x] - + 32*(-1 + 2*x)*H[0, -1, 1, x] - (80*(-5 + 2*x)*H[0, 0, -1, x])/3 - + (16*(21 + 23*x)*H[0, 0, 1, x])/3 - 32*(-1 + 2*x)*H[0, 1, -1, x] + + (64*(-2 + x)*H[0, 1, 1, x])/3) + + z2*((2*(1080 + 7656*x + 21800*x^2 - 37561*x^3 - 28192*x^4 + 32571*x^5 + + 810*x^6))/(81*(-1 + x)^2*x*(1 + x)) - (16*(1 + 4*x)*z3)/3 - + (8*(24 + 73*x + 105*x^2 + 74*x^3 + 26*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + 8*(1 + x)*H[0, x]^3 + (4*(8 + 35*x - 114*x^2 + 63*x^3)*H[1, x]^2)/ + (9*(-1 + x)*x) + H[0, x]^2* + ((-4*(61 - 174*x - 89*x^2 + 174*x^3 + 26*x^4))/(9*(-1 + x)*(1 + x)) - + 8*(-1 + x)*H[1, x]) + (8*(-26 + 270*x + 131*x^2 - 310*x^3 - 165*x^4 + + 40*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + H[1, x]*((8*(175 + 647*x - 1839*x^2 + 1058*x^3 + 4*x^4))/ + (27*(-1 + x)*x) - 32*(-1 + x)*H[0, -1, x]) - + (8*(142 - 104*x - 491*x^2 + 76*x^3 + 415*x^4 + 50*x^5)*H[0, 1, x])/ + (9*(-1 + x)*x*(1 + x)) + H[-1, x]* + ((-16*(15 + 11*x + 71*x^2 + 71*x^3 + 2*x^4))/(9*x^2) + + (8*(22 + 237*x + 435*x^2 + 268*x^3 + 36*x^4)*H[0, x])/(9*x*(1 + x)) + + 8*(1 + x)*H[0, x]^2 + 32*(1 + x)*H[0, 1, x]) + + H[0, x]*((-4*(1184 + 673*x - 1396*x^2 - 969*x^3 + 112*x^4))/ + (27*(-1 + x)*(1 + x)) + (16*(63 - 31*x - 111*x^2 + 74*x^3 + 21*x^4)* + H[1, x])/(9*(-1 + x)*x) - (32*(-2 + 5*x)*H[0, -1, x])/3 - + (32*(8 + 5*x)*H[0, 1, x])/3) - (64*(-1 + x)*H[0, -1, -1, x])/3 - + 64*H[0, -1, 1, x] + (16*(-43 + 13*x)*H[0, 0, -1, x])/3 + + (32*(17 + 12*x)*H[0, 0, 1, x])/3 - 64*H[0, 1, -1, x] - + (80*(1 + x)*H[0, 1, 1, x])/3) + + H[0, 1, x]*((-2*(-1431 - 19960*x + 70276*x^2 - 75515*x^3 + 25388*x^4 + + 324*x^5))/(81*(-1 + x)^2*x) - 3072*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x] - 3072*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] + 64*(-1 + x)*H[0, -1, -1, x] + + (160*(7 + x)*H[0, 0, -1, x])/3 - (64*(17 + 2*x)*H[0, 0, 1, x])/3 + + 64*(1 + x)*H[0, 1, -1, x] + (176*(1 + x)*H[0, 1, 1, x])/3) - + (32*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[0, -1, -1, -1, x])/ + (9*x*(1 + x)) + (32*(1 + x)*(14 + 43*x + 14*x^2)*H[0, -1, -1, 1, x])/ + (9*x) - (16*(28 + 150*x - 363*x^2 - 156*x^3 + 339*x^4 + 18*x^5)* + H[0, -1, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + + (32*(1 + x)*(14 + 43*x + 14*x^2)*H[0, -1, 1, -1, x])/(9*x) - + (128*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) - + (16*(66 + 128*x + 75*x^2 + 49*x^3 + 28*x^4)*H[0, 0, -1, -1, x])/ + (9*x*(1 + x)) + (16*(22 + 3*x - 59*x^2 + 10*x^3)*H[0, 0, -1, 1, x])/ + (3*x) - (8*(-116 + 317*x - 861*x^2 - 687*x^3 + 667*x^4 + 200*x^5)* + H[0, 0, 0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + (16*(22 - 157*x - 953*x^2 - 8*x^3 + 824*x^4 + 86*x^5)*H[0, 0, 0, 1, x])/ + (9*(-1 + x)*x*(1 + x)) + + H[1, x]*((-2*(1080 + 13157*x - 14191*x^2 - 33994*x^3 - 39006*x^4 + + 241128*x^5 - 240696*x^6 + 73440*x^7))/(81*(-1 + x)*x) + + (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (8*(-1 + x)*(-10 + 5*x - 15*x^2 + 12*x^3)*H[0, -1, x])/(3*x^2) + + 32*(-1 + x)*H[0, -1, x]^2 + (4*(-60 + 6*x - 967*x^2 + 2194*x^3 - + 1251*x^4 + 48*x^5)*H[0, 1, x])/(9*(-1 + x)*x^2) - + (64*(70 - 135*x + 65*x^2 + 4*x^3)*H[0, 0, -1, x])/(9*(-1 + x)) + + (16*(-26 + 268*x - 429*x^2 + 189*x^3 + 6*x^4)*H[0, 0, 1, x])/ + (9*(-1 + x)*x) - (16*(6 - 46*x + 83*x^2 - 43*x^3 + 2*x^4)* + H[0, 1, 1, x])/(3*(-1 + x)*x) + 384*(-1 + x)*H[0, 0, 0, -1, x] - + 288*(-1 + x)*H[0, 0, 0, 1, x]) + + H[-1, x]*((-8*(-10 + 27*x + 96*x^2 + 63*x^3 + 8*x^4)*H[0, x]^3)/ + (27*x*(1 + x)) - (8*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)* + H[0, -1, x])/(27*x^2) - (8*(1 + x)*(90 + 127*x - 175*x^2 + 136*x^3)* + H[0, 1, x])/(27*x^2) - 32*(1 + x)*H[0, 1, x]^2 + + H[0, x]^2*((2*(270 + 277*x + 1524*x^2 + 1485*x^3 + 88*x^4))/(27*x^2) + + 16*(1 + x)*H[0, 1, x]) + (32*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)* + H[0, -1, -1, x])/(9*x*(1 + x)) - (32*(1 + x)*(14 + 43*x + 14*x^2)* + H[0, -1, 1, x])/(9*x) + (16*(66 + 128*x + 75*x^2 + 49*x^3 + 28*x^4)* + H[0, 0, -1, x])/(9*x*(1 + x)) - (16*(22 + 3*x - 11*x^2 + 10*x^3)* + H[0, 0, 1, x])/(3*x) - (32*(1 + x)*(14 + 43*x + 14*x^2)* + H[0, 1, -1, x])/(9*x) + (128*(1 + x)^3*H[0, 1, 1, x])/(9*x) + + H[0, x]*((16*(927 + 5978*x + 8862*x^2 + 4340*x^3 + 81*x^4))/ + (81*x*(1 + x)) + (8*(-1 + x)*(-10 + 5*x - 15*x^2 + 12*x^3)*H[1, x])/ + (3*x^2) - (16*(44 + 11*x - 11*x^2 + 28*x^3)*H[0, -1, x])/(9*x) + + (16*(22 - 21*x - 42*x^2 + 4*x^3)*H[0, 1, x])/(9*x) - + 32*(1 + x)*H[0, 0, 1, x] + 64*(1 + x)*H[0, 1, 1, x]) - + 32*(1 + x)*H[0, 0, 0, 1, x]) + (16*(22 + 3*x - 11*x^2 + 10*x^3)* + H[0, 0, 1, -1, x])/(3*x) - + (16*(26 - 32*x - 297*x^2 + 16*x^3 + 281*x^4 + 42*x^5)*H[0, 0, 1, 1, x])/ + (9*(-1 + x)*x*(1 + x)) + (32*(1 + x)*(14 + 43*x + 14*x^2)* + H[0, 1, -1, -1, x])/(9*x) - (128*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) - + (128*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + + (8*(132 - 487*x + 684*x^2 - 353*x^3 + 44*x^4)*H[0, 1, 1, 1, x])/ + (9*(-1 + x)*x) + H[0, x]* + ((-2*(360 - 1405*x - 12835*x^2 + 2628*x^3 - 13002*x^4 + 80376*x^5 - + 80232*x^6 + 24480*x^7))/(27*(-1 + x)*x) + + 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + + 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + + (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (2*(36 + 341*x - 399*x^2 + 24*x^3)*H[1, x]^2)/(9*x) + + (4*(12 - 81*x + 123*x^2 - 80*x^3 + 10*x^4)*H[1, x]^3)/(27*(-1 + x)*x) + + (16*(5 + 9*x^2)*H[-1, 1, x])/x - (128*(-1 + x)*H[0, -1, x]^2)/3 - + (4*(90 - 531*x - 862*x^2 + 1601*x^3 + 422*x^4 - 1276*x^5 + 216*x^6)* + H[0, 1, x])/(27*(-1 + x)*x^2*(1 + x)) + (8*(41 + 5*x)*H[0, 1, x]^2)/ + 3 + H[0, -1, x]*((-4*(-270 + 11*x + 226*x^2 - 3164*x^3 + 168*x^4 + + 3421*x^5 + 72*x^6))/(27*(-1 + x)*x^2*(1 + x)) + + (64*(-11 + x)*H[0, 1, x])/3) + + (16*(-82 + 3*x + 202*x^2 - 63*x^3 - 152*x^4 + 32*x^5)*H[0, -1, -1, x])/ + (9*(-1 + x)*x*(1 + x)) - (16*(-22 + 213*x - 243*x^2 + 48*x^3 + 12*x^4)* + H[0, -1, 1, x])/(9*(-1 + x)*x) + + (16*(-42 + 159*x - 33*x^2 - 274*x^3 - 12*x^4 + 64*x^5)*H[0, 0, -1, x])/ + (9*(-1 + x)*x*(1 + x)) - (8*(44 - 113*x - 970*x^2 - 11*x^3 + 846*x^4 + + 84*x^5)*H[0, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + + H[1, x]*((2*(2511 - 9631*x + 7671*x^2 - 4153*x^3 + 162*x^4))/ + (81*(-1 + x)*x) + (32*(70 - 135*x + 65*x^2 + 4*x^3)*H[0, -1, x])/ + (9*(-1 + x)) - (8*(52 + 218*x - 507*x^2 + 255*x^3 + 38*x^4)* + H[0, 1, x])/(9*(-1 + x)*x) - 64*(-1 + x)*H[0, -1, -1, x] - + 224*(-1 + x)*H[0, 0, -1, x] + 128*(-1 + x)*H[0, 0, 1, x]) - + (16*(-22 + 213*x - 315*x^2 + 120*x^3 + 12*x^4)*H[0, 1, -1, x])/ + (9*(-1 + x)*x) + (8*(52 + 562*x - 337*x^2 - 540*x^3 + 283*x^4 + 56*x^5)* + H[0, 1, 1, x])/(9*(-1 + x)*x*(1 + x)) - + (256*(-1 + x)*H[0, -1, -1, -1, x])/3 + 64*(-1 + x)*H[0, -1, -1, 1, x] + + (32*(17 + 3*x)*H[0, -1, 0, 1, x])/3 + 64*(-1 + x)*H[0, -1, 1, -1, x] - + 64*(1 + x)*H[0, -1, 1, 1, x] + (64*(-8 + 5*x)*H[0, 0, -1, -1, x])/3 + + (128*(8 + 5*x)*H[0, 0, -1, 1, x])/3 - (32*(64 + x)*H[0, 0, 0, -1, x])/ + 3 + 16*(27 + 35*x)*H[0, 0, 0, 1, x] + (128*(8 + 5*x)*H[0, 0, 1, -1, x])/ + 3 - (176*(3 + 5*x)*H[0, 0, 1, 1, x])/3 + + 64*(-1 + x)*H[0, 1, -1, -1, x] - 64*(1 + x)*H[0, 1, -1, 1, x] - + 64*(1 + x)*H[0, 1, 1, -1, x] + (32*(1 + x)*H[0, 1, 1, 1, x])/3) - + (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 - + (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] - + (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - + (32*(-23 + 17*x)*H[0, 0, -1, 0, -1, x])/3 + + (32*(-55 + 9*x)*H[0, 0, -1, 0, 1, x])/3 + + 128*(1 + x)*H[0, 0, -1, 1, 1, x] - 32*(-23 + 17*x)*H[0, 0, 0, -1, -1, x] - + 32*(45 + 11*x)*H[0, 0, 0, -1, 1, x] + + (64*(59 + 26*x)*H[0, 0, 0, 0, -1, x])/3 - + (16*(137 + 213*x)*H[0, 0, 0, 0, 1, x])/3 - + 32*(45 + 11*x)*H[0, 0, 0, 1, -1, x] + 80*(21 + 11*x)*H[0, 0, 0, 1, 1, x] - + (64*(23 + 6*x)*H[0, 0, 1, 0, -1, x])/3 + + (32*(68 + 21*x)*H[0, 0, 1, 0, 1, x])/3 - + 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + + CF^2*TF*((448*B4)/3 - (16*(180 + 2181*x - 7221*x^2 + 7404*x^3 - 4232*x^4 + + 960*x^5))/(27*x) - (32*(137 + 5*x)*z5)/3 - + 3072*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 - + (1024*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1)}, x]) + + (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(3*x^2) + + (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(3*x^2) + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 12288*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + (256*(1 + x)*H[-1, x]^3*H[0, x])/3 - (2*(-7 + 3*x)*H[0, x]^4)/9 + + (2*(1 + x)*H[0, x]^5)/15 + z4*((20*(-277 + 27*x))/3 - + (16*(109 + 61*x)*H[0, x])/3) - (164*(-1 + x)*H[1, x]^3)/9 - + (10*(-1 + x)*H[1, x]^4)/9 + (32*(10 + 23*x)*H[0, -1, x]^2)/3 + + H[-1, x]^2*((-16*(1 + x)*(10 + 14*x + 33*x^2)*H[0, x])/(3*x^2) - + (320*(1 + x)*H[0, x]^2)/3 - 256*(1 + x)*H[0, -1, x]) - + (16*(-41 + 17*x)*H[0, 1, x]^2)/3 + + H[1, x]^2*((-692*(-1 + x))/3 - (16*(-1 + x)*H[0, 1, x])/3) + + z3*((-4*(147 - 167*x + 24*x^2))/3 - 384*(1 + x)*H[-1, x] + + (16*(-196 + 13*x)*H[0, x])/3 - (8*(-1 + 15*x)*H[0, x]^2)/3 - + (16*(-1 + x)*H[1, x])/3 + 192*(-1 + x)*H[0, -1, x] - + (32*(1 + x)*H[0, 1, x])/3) + H[0, x]^3*((-2*(5 + x)*(7 + 16*x))/9 - + (208*(-1 + x)*H[1, x])/9 + (64*(-1 + x)*H[0, -1, x])/9 + + (32*(1 + x)*H[0, 1, x])/3) - (32*(1 + x)*(10 + 14*x + 33*x^2)* + H[0, -1, -1, x])/(3*x^2) + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)* + H[0, -1, 1, x])/(3*x^2) + (16*(30 + 96*x + 153*x^2 + 175*x^3)* + H[0, 0, -1, x])/(3*x^2) + (8*(-20 + 56*x + 47*x^2 + 163*x^3 + 64*x^4)* + H[0, 0, 1, x])/(3*x^2) + H[0, -1, x]* + ((-32*(1 + x)*(97 + 35*x + 19*x^2))/(9*x) + (256*(-5 + 3*x)*H[0, 1, x])/ + 3 + 256*(-1 + x)*H[0, -1, -1, x] + 128*(-1 + x)*H[0, 0, -1, x] - + 256*(-1 + x)*H[0, 0, 1, x]) + + H[-1, x]*((8*(1 + x)*(30 + 50*x + 103*x^2 + 8*x^3)*H[0, x]^2)/(3*x^2) - + (128*(1 + x)*H[0, x]^3)/9 + (32*(1 + x)*(10 + 14*x + 33*x^2)* + H[0, -1, x])/(3*x^2) - (64*(1 + x)*(5 + 10*x + 19*x^2 + 3*x^3)* + H[0, 1, x])/(3*x^2) + H[0, x]*((32*(1 + x)*(97 + 35*x + 19*x^2))/ + (9*x) + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[1, x])/(3*x^2) + + (1024*(1 + x)*H[0, -1, x])/3 - 256*(1 + x)*H[0, 1, x]) + + 512*(1 + x)*H[0, -1, -1, x] - 256*(1 + x)*H[0, 0, -1, x] + + 512*(1 + x)*H[0, 0, 1, x]) + (64*(1 + x)*(5 + 10*x + 19*x^2 + 3*x^3)* + H[0, 1, -1, x])/(3*x^2) - (32*(20 - 48*x + 60*x^2 - 65*x^3 + 6*x^4)* + H[0, 1, 1, x])/(3*x^2) + + H[1, x]*((-8*(-1 + x)*(120 - 1785*x - 2536*x^2 + 8176*x^3 - 7312*x^4 + + 1920*x^5))/(9*x) + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1)}, x] - + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[0, -1, x])/(3*x^2) + + (16*(20 - 48*x + 107*x^2 - 79*x^3 + 8*x^4)*H[0, 1, x])/(3*x^2) - + 512*(-1 + x)*H[0, 0, -1, x] + 96*(-1 + x)*H[0, 0, 1, x] + + (416*(-1 + x)*H[0, 1, 1, x])/3) + + H[0, x]^2*((-2*(240 + 1593*x + 1835*x^2 + 152*x^3))/(9*x) - + 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1)}, x] - + (4*(-1 + x)*(-20 + 36*x + 13*x^2 + 8*x^3)*H[1, x])/(3*x^2) + + 8*(-1 + x)*H[1, x]^2 + (16*(38 + 51*x)*H[0, -1, x])/3 + + (16*(-15 + 32*x)*H[0, 1, x])/3 + (320*(-1 + x)*H[0, -1, -1, x])/3 - + (256*(-3 + 2*x)*H[0, 0, -1, x])/3 - (16*(31 + 23*x)*H[0, 0, 1, x])/3 - + (32*(1 + x)*H[0, 1, 1, x])/3) + + H[0, 1, x]*((-8*(474 - 183*x + 1405*x^2))/(9*x) - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1)}, x] + 256*(1 + x)*H[0, 0, -1, x] - + (448*(1 + x)*H[0, 0, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, x])/3) + + z2*((2*(480 + 909*x + 7507*x^2 + 304*x^3))/(9*x) - 16*(13 + 5*x)*z3 + + 128*(1 + x)*H[-1, x]^2 - (4*(103 + 17*x)*H[0, x]^2)/3 + + (4*(1 + x)*H[0, x]^3)/9 + H[-1, x]* + ((-16*(1 + x)*(20 + 34*x + 71*x^2 + 6*x^3))/(3*x^2) + + (256*(1 + x)*H[0, x])/3) + (4*(-24 + 131*x - 147*x^2 + 8*x^3)*H[1, x])/ + (3*x) - 84*(-1 + x)*H[1, x]^2 - (160*(6 + 7*x)*H[0, -1, x])/3 - + (8*(5 + 23*x)*H[0, 1, x])/3 + H[0, x]*((-2*(265 + 701*x))/3 - + (176*(-1 + x)*H[1, x])/3 - (128*(-1 + x)*H[0, -1, x])/3 + + 32*(1 + x)*H[0, 1, x]) - 128*(-1 + x)*H[0, -1, -1, x] + + 128*(-3 + 2*x)*H[0, 0, -1, x] + (32*(13 + x)*H[0, 0, 1, x])/3 + + (176*(1 + x)*H[0, 1, 1, x])/3) - 512*(1 + x)*H[0, -1, -1, -1, x] - + 512*x*H[0, -1, 0, 1, x] + 256*(1 + x)*H[0, 0, -1, -1, x] - + 512*(1 + x)*H[0, 0, -1, 1, x] + (32*(98 + 23*x)*H[0, 0, 0, -1, x])/3 + + 96*(-1 + 6*x)*H[0, 0, 0, 1, x] - 512*(1 + x)*H[0, 0, 1, -1, x] + + (160*(-3 + 7*x)*H[0, 0, 1, 1, x])/3 - (16*(-67 + 53*x)*H[0, 1, 1, 1, x])/ + 3 + H[0, x]*((-8*(-120 + 973*x + 880*x^2 - 10712*x^3 + 15488*x^4 - + 9232*x^5 + 1920*x^6))/(9*x) + 2048*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + + 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + + (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (8*(-1 + x)*(-13 + 4*x)*H[1, x]^2)/3 - (176*(-1 + x)*H[1, x]^3)/9 + + (128*(15 + 22*x^2)*H[-1, 1, x])/(3*x) - (256*(-1 + x)*H[0, -1, x]^2)/3 - + (16*(-10 + 28*x - 4*x^2 + 21*x^3 + 12*x^4)*H[0, 1, x])/(3*x^2) + + 32*(1 + x)*H[0, 1, x]^2 + H[1, x]*((-8*(-1 + x)*(118 + 47*x))/(3*x) + + 256*(-1 + x)*H[0, -1, x] - 32*(-1 + x)*H[0, 1, x]) + + H[0, -1, x]*((-16*(30 + 88*x + 153*x^2 + 143*x^3 + 4*x^4))/(3*x^2) - + 128*(1 + x)*H[0, 1, x]) - (832*(2 + 3*x)*H[0, -1, -1, x])/3 + + (2048*H[0, -1, 1, x])/3 - (128*(17 + 14*x)*H[0, 0, -1, x])/3 - + 32*(-8 + 15*x)*H[0, 0, 1, x] + (2048*H[0, 1, -1, x])/3 - + (128*(3 + x)*H[0, 1, 1, x])/3 - 256*(-1 + x)*H[0, -1, -1, -1, x] + + 256*x*H[0, -1, 0, 1, x] + 256*(-1 + x)*H[0, 0, -1, -1, x] + + 256*(2 + x)*H[0, 0, -1, 1, x] + 128*(-11 + 5*x)*H[0, 0, 0, -1, x] + + 256*(3 + 2*x)*H[0, 0, 0, 1, x] + 256*(2 + x)*H[0, 0, 1, -1, x] - + (256*(1 + x)*H[0, 0, 1, 1, x])/3 + 64*(1 + x)*H[0, 1, 1, 1, x]) - + 512*(-1 + x)*H[0, -1, 0, -1, -1, x] - 1024*(-1 + x)* + H[0, 0, -1, -1, -1, x] - 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - + 768*H[0, 0, -1, 0, 1, x] - 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - + 2304*H[0, 0, 0, -1, 1, x] - (2048*(-4 + x)*H[0, 0, 0, 0, -1, x])/3 - + (128*(31 + 19*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*H[0, 0, 0, 1, -1, x] + + (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*H[0, 0, 1, 0, -1, x] + + 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + + CA*(TF^2*((8*(433567 + 493927*x - 565164*x^2 - 117720*x^3 + 138240*x^4))/ + 18225 - (16*(119 + 676*x)*z3)/45 + + (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + + 61440*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ + (675*(-((-1 + x)*x))^(3/2)) + + (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + + 61440*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ + (675*(-((-1 + x)*x))^(3/2)) - + (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/45 - + (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/45 - + (16*(-35 + x)*H[0, x]^3)/405 - (8*(-143 + 178*x)*H[1, x]^2)/135 + + H[0, x]^2*((8*(-4250 - 1317*x + 5027*x^2))/(2025*(-1 + x)) - + (32*x*H[1, x])/15) + z2*((-8*(17500 - 49809*x + 31229*x^2))/ + (2025*(-1 + x)) + (16*(145 + 217*x)*H[0, x])/135 + + (64*x*H[1, x])/15) + (8*(10165 - 29589*x + 18344*x^2)*H[0, 1, x])/ + (2025*(-1 + x)) + H[1, x]* + ((32*(-2963 - 8767*x + 38844*x^2 - 21144*x^3 - 15570*x^4 + 11520*x^5))/ + 2025 - (64*x*H[0, 1, x])/15) + + H[0, x]*((16*(-7674 + 25658*x - 96497*x^2 + 119976*x^3 - 11148*x^4 - + 54180*x^5 + 23040*x^6))/(2025*(-1 + x)) - + (8*(-491 + 471*x)*H[1, x])/135 + (8*(169 + 304*x)*H[0, 1, x])/135) - + (304*(11 + 20*x)*H[0, 0, 1, x])/135 + (8*(89 + 296*x)*H[0, 1, 1, x])/ + 135 + NF*((-8*(-24449 + 31393*x))/729 + (64*(-1 + 6*x)*z3)/9 - + (4*(-584 + 25*x)*H[0, x]^2)/81 + (224*(1 + x)*H[0, x]^3)/81 + + z2*((-40*(8 + 65*x))/81 - (32*(1 + x)*H[0, x])/27) - + (8*(-281 + 137*x)*H[1, x])/81 + (4*(-41 + 25*x)*H[1, x]^2)/27 + + (8*(85 + 232*x)*H[0, 1, x])/81 + + H[0, x]*((-8*(1220 - 1337*x + 177*x^2))/(81*(-1 + x)) - + (8*(-41 + 45*x)*H[1, x])/27 + (128*(1 + x)*H[0, 1, x])/27) - + (128*(1 + x)*H[0, 0, 1, x])/27 - (128*(1 + x)*H[0, 1, 1, x])/27)) + + CF*TF*(-96*B4*(1 + 2*x) + (4*(-6480 + 691055*x - 1544560*x^2 + + 762245*x^3 + 282708*x^4 - 279576*x^5 + 87264*x^6))/(243*(-1 + x)*x) + + (16*(883 + 111*x)*z5)/3 + (1024*(-21 + 19*x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2)/3 + + (1024*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/ + 3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* + ((-64*(320 - 985*x + 3701*x^2 - 5670*x^3 + 2592*x^4))/ + (9*Sqrt[-((-1 + x)*x)]) + (2048*(-21 + 19*x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* + ((-64*(320 - 985*x + 3701*x^2 - 5670*x^3 + 2592*x^4))/ + (9*Sqrt[-((-1 + x)*x)]) + 8192*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + x]) - (256*(40 - 94*x + 259*x^2 - 677*x^3 + 456*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) - + (256*(40 - 94*x + 259*x^2 - 677*x^3 + 456*x^4)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x])/(3*(-1 + x)*x^2) - + (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 - + (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - + 16384*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 24576*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] - + (32*(1 + x)*(4 + 41*x + 4*x^2)*H[-1, x]^3*H[0, x])/(27*x) - + (4*(-190 - 49*x + 12*x^2)*H[0, x]^4)/27 - (4*(-9 + 5*x)*H[0, x]^5)/15 + + z4*((-4*(-10838 - 3563*x + 72*x^2))/9 + (8*(550 + 19*x)*H[0, x])/3) + + (532*(-1 + x)*H[1, x]^3)/27 + (10*(-1 + x)*H[1, x]^4)/9 + + (16*(38 + 87*x - 177*x^2 + 4*x^3)*H[0, -1, x]^2)/(9*x) - + (16*(-52 + 279*x - 114*x^2 + 10*x^3)*H[0, 1, x]^2)/(9*x) + + z3*((4*(11627 - 8151*x - 3648*x^2 + 604*x^3))/(27*(-1 + x)) - + (16*(1 + x)*(50 + 25*x + 32*x^2)*H[-1, x])/(9*x) + + (16*(373 - 104*x + 76*x^2)*H[0, x])/9 + (16*(-34 + 5*x)*H[0, x]^2)/3 + + (16*(68 - 147*x + 111*x^2 + 4*x^3)*H[1, x])/(9*x) - + (256*(-1 + x)*H[0, -1, x])/3 - (128*(1 + x)*H[0, 1, x])/3) + + H[0, x]^3*((4*(3755 - 1081*x + 52*x^2))/81 + + (8*(-1 + x)*(44 + 161*x + 8*x^2)*H[1, x])/(27*x) - + (176*(-1 + x)*H[0, -1, x])/9 - (208*(1 + x)*H[0, 1, x])/9) + + H[-1, x]^2*((-8*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, x])/ + (27*x^2) - (8*(1 + x)*(22 - x + 22*x^2)*H[0, x]^2)/(9*x) + + (32*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, x])/(9*x) - + (448*(1 + x)^3*H[0, 1, x])/(9*x)) + + H[1, x]^2*((4*(-1 + x)*(-477 - 74*x + 27*x^2))/(27*x) + + (16*(-2 - 33*x + 31*x^2 + 2*x^3)*H[0, 1, x])/(3*x)) - + (16*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, -1, -1, x])/ + (27*x^2) - (16*(180 - 323*x + 294*x^2 - 1101*x^3 + 190*x^4)* + H[0, -1, 1, x])/(27*x^2) - (8*(540 + 565*x + 1827*x^2 + 3546*x^3 + + 56*x^4)*H[0, 0, -1, x])/(27*x^2) + H[0, -1, x]* + ((16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - + (64*(-37 + 34*x)*H[0, 1, x])/3 - (512*(-1 + x)*H[0, -1, -1, x])/3 + + (256*(-1 + x)*H[0, 0, -1, x])/3) - + (8*(180 - 1179*x - 11164*x^2 + 9321*x^3 + 1778*x^4 + 920*x^5)* + H[0, 0, 1, x])/(27*(-1 + x)*x^2) - + (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, -1, x])/(27*x^2) + + (16*(-360 + 684*x - 2737*x^2 + 4797*x^3 - 2474*x^4 + 162*x^5)* + H[0, 1, 1, x])/(27*(-1 + x)*x^2) + + H[0, 1, x]*((8*(918 - 34900*x + 102373*x^2 - 103421*x^3 + 35084*x^4 + + 162*x^5))/(81*(-1 + x)^2*x) + 8192*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x] + 8192*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] - (1664*(1 + x)*H[0, 0, -1, x])/3 + + (1312*(1 + x)*H[0, 0, 1, x])/3 - 192*(1 + x)*H[0, 1, 1, x]) + + z2*((-4*(2160 + 8377*x - 32965*x^2 + 34247*x^3 - 13205*x^4 + 1818*x^5))/ + (81*(-1 + x)^2*x) + (8*(19 + 17*x)*z3)/3 + + (16*(1 + x)*(8 + 5*x + 8*x^2)*H[-1, x]^2)/(3*x) + + (8*(-148 + 155*x + 36*x^2)*H[0, x]^2)/9 - (8*(23 + 41*x)*H[0, x]^3)/ + 9 + H[-1, x]*((8*(1 + x)*(120 + 86*x + 163*x^2 + 26*x^3))/(9*x^2) - + (8*(1 + x)*(44 + 229*x + 80*x^2)*H[0, x])/(9*x)) - + (4*(808 + 1079*x - 4854*x^2 + 2771*x^3 + 52*x^4)*H[1, x])/ + (27*(-1 + x)*x) - (4*(-16 - 111*x + 87*x^2 + 16*x^3)*H[1, x]^2)/ + (9*x) - (8*(52 - 399*x - 411*x^2 + 64*x^3)*H[0, -1, x])/(9*x) + + (8*(-284 - 10*x + 623*x^2 + 72*x^3)*H[0, 1, x])/(9*x) + + H[0, x]*((28*(-767 - 941*x + 32*x^2))/27 - + (8*(-1 + x)*(84 + 179*x + 24*x^2)*H[1, x])/(3*x) + + (112*(-1 + x)*H[0, -1, x])/3 + (688*(1 + x)*H[0, 1, x])/3) + + (256*(-1 + x)*H[0, -1, -1, x])/3 - (32*(-55 + 19*x)*H[0, 0, -1, x])/ + 3 - (16*(115 + 91*x)*H[0, 0, 1, x])/3 + (208*(1 + x)*H[0, 1, 1, x])/ + 3) + H[0, x]^2*((4*(-1080 - 11923*x - 9906*x^2 + 22243*x^3 + + 747*x^4))/(81*(-1 + x)*x) + 4096*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x] + 4096*(1 + x)* + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] + (4*(20 - 63*x - 297*x^2 + 322*x^3 + 12*x^4)* + H[1, x])/(3*x^2) - (4*(-1 + x)*(52 + 205*x + 16*x^2)*H[1, x]^2)/ + (9*x) + (16*(26 - 111*x - 189*x^2 + 22*x^3)*H[0, -1, x])/(9*x) - + (8*(-44 + 83*x + 686*x^2 + 24*x^3)*H[0, 1, x])/(9*x) - + 64*(-1 + x)*H[0, -1, -1, x] + (64*(-19 + 10*x)*H[0, 0, -1, x])/3 + + (32*(23 + 28*x)*H[0, 0, 1, x])/3 + (272*(1 + x)*H[0, 1, 1, x])/3) + + H[-1, x]*((-4*(1 + x)*(540 + 457*x + 26*x^2 + 160*x^3)*H[0, x]^2)/ + (27*x^2) + (8*(1 + x)*(-20 + 179*x + 16*x^2)*H[0, x]^3)/(27*x) + + (16*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, -1, x])/(27*x^2) + + (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, x])/(27*x^2) + + H[0, x]*((-16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - + (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[1, x])/(3*x^2) + + (32*(1 + x)*(44 + 73*x + 26*x^2)*H[0, -1, x])/(9*x) - + (32*(1 + x)*(22 + 35*x + 4*x^2)*H[0, 1, x])/(9*x)) - + (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, x])/(9*x) + + (896*(1 + x)^3*H[0, -1, 1, x])/(9*x) - + (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, x])/(3*x) + + (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, x])/(3*x) + + (896*(1 + x)^3*H[0, 1, -1, x])/(9*x) - (256*(1 + x)^3*H[0, 1, 1, x])/ + (9*x)) + H[1, x]*((8*(1080 - 557*x - 4313*x^2 + 34345*x^3 - + 137403*x^4 + 231804*x^5 - 170532*x^6 + 45360*x^7))/ + (81*(-1 + x)*x) - (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[0, -1, x])/(3*x^2) - + (16*(-20 + 35*x - 182*x^2 + 362*x^3 - 203*x^4 + 12*x^5)*H[0, 1, x])/ + (3*(-1 + x)*x^2) + (3584*(-1 + x)*H[0, 0, -1, x])/3 + + (16*(-52 + 465*x - 405*x^2 + 16*x^3)*H[0, 0, 1, x])/(9*x) - + (16*(12 - 131*x + 111*x^2)*H[0, 1, 1, x])/(3*x)) + + (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, -1, x])/(9*x) - + (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + + (32*(-28 - 291*x + 255*x^2 + 10*x^3)*H[0, -1, 0, 1, x])/(9*x) - + (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + + (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, -1, x])/(3*x) - + (64*(11 + 30*x + 5*x^3)*H[0, 0, -1, 1, x])/(3*x) + + (32*(58 - 192*x + 501*x^2 + 70*x^3)*H[0, 0, 0, -1, x])/(9*x) - + (64*(-11 + 452*x + 560*x^2 + 27*x^3)*H[0, 0, 0, 1, x])/(9*x) - + (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, -1, x])/(3*x) + + (16*(-52 - 38*x + 199*x^2 + 44*x^3)*H[0, 0, 1, 1, x])/(9*x) - + (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) - + (16*(-132 + 641*x - 451*x^2 + 24*x^3)*H[0, 1, 1, 1, x])/(9*x) + + H[0, x]*((8*(3240 + 67018*x + 211920*x^2 - 190999*x^3 - 412209*x^4 + + 695412*x^5 - 511596*x^6 + 136080*x^7))/(243*(-1 + x)*x) - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^ + 2 - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, + x]*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 - + (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + (8*(18 + 269*x - 311*x^2 + 18*x^3)*H[1, x]^2)/(9*x) - + (16*(-1 + x)*(2 + 7*x + 2*x^2)*H[1, x]^3)/(9*x) - + (32*(45 + 71*x^2)*H[-1, 1, x])/(3*x) + (32*(-1 + x)*H[0, -1, x]^2)/3 + + (8*(180 - 963*x - 7894*x^2 + 7725*x^3 + 556*x^4 + 324*x^5)*H[0, 1, x])/ + (27*(-1 + x)*x^2) - (560*(1 + x)*H[0, 1, x]^2)/3 + + H[0, -1, x]*((8*(540 + 781*x + 1155*x^2 + 1866*x^3 + 108*x^4))/ + (27*x^2) + (832*(1 + x)*H[0, 1, x])/3) + + H[1, x]*((-8*(-54 - 10417*x + 10480*x^2 + 27*x^3))/(27*x) - + (1792*(-1 + x)*H[0, -1, x])/3 + (16*(-52 - 333*x + 357*x^2 + 16*x^3)* + H[0, 1, x])/(9*x)) - (64*(41 + 102*x - 39*x^2 + 15*x^3)* + H[0, -1, -1, x])/(9*x) + (32*(22 - 165*x + 171*x^2 + 4*x^3)* + H[0, -1, 1, x])/(9*x) - (16*(28 - 99*x + 7*x^2 + 32*x^3)* + H[0, 0, -1, x])/(3*x) + (16*(-44 + 776*x + 1349*x^2 + 48*x^3)* + H[0, 0, 1, x])/(9*x) + (32*(22 - 165*x + 243*x^2 + 4*x^3)* + H[0, 1, -1, x])/(9*x) - (16*(-52 - 713*x + 523*x^2 + 28*x^3)* + H[0, 1, 1, x])/(9*x) + (512*(-1 + x)*H[0, -1, -1, -1, x])/3 - + (832*(1 + x)*H[0, -1, 0, 1, x])/3 - (896*(-1 + x)*H[0, 0, -1, -1, x])/ + 3 - (128*(19 + 13*x)*H[0, 0, -1, 1, x])/3 - + (32*(-195 + 43*x)*H[0, 0, 0, -1, x])/3 - + (32*(79 + 133*x)*H[0, 0, 0, 1, x])/3 - + (128*(19 + 13*x)*H[0, 0, 1, -1, x])/3 + + (1280*(1 + x)*H[0, 0, 1, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, 1, x])/3) + + (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + + (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + + (256*(8 + 5*x)*H[0, 0, -1, 0, 1, x])/3 + + 640*(-1 + x)*H[0, 0, 0, -1, -1, x] + 128*(19 + 13*x)* + H[0, 0, 0, -1, 1, x] - (256*(46 + 3*x)*H[0, 0, 0, 0, -1, x])/3 + + 128*(9 + 22*x)*H[0, 0, 0, 0, 1, x] + 128*(19 + 13*x)* + H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + + (128*(19 + 13*x)*H[0, 0, 1, 0, -1, x])/3 - + (2464*(1 + x)*H[0, 0, 1, 0, 1, x])/3 + 1120*(1 + x)* + H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3)); diff --git a/extras/ome_n3lo/n3lo_matching.tar.gz b/extras/ome_n3lo/notebooks/n3lo_matching.tar.gz similarity index 100% rename from extras/ome_n3lo/n3lo_matching.tar.gz rename to extras/ome_n3lo/notebooks/n3lo_matching.tar.gz From 719f1f0a097a631ac7e0c9776b4a499c801bb238 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 13:26:25 +0100 Subject: [PATCH 04/18] subtract large-n limit --- extras/ome_n3lo/convert_ome_xspace.py | 11 +- .../{largex_limit.py => large_n_limit.py} | 0 ...pansion.nb => Agg_Aqq_largeN_expansion.nb} | 113 +++++++++++++++--- 3 files changed, 105 insertions(+), 19 deletions(-) rename extras/ome_n3lo/{largex_limit.py => large_n_limit.py} (100%) rename extras/ome_n3lo/notebooks/{Agg_Aqq_largex_expansion.nb => Agg_Aqq_largeN_expansion.nb} (91%) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 3cb0739d9..e127713bc 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -5,6 +5,8 @@ from ekore.operator_matrix_elements.unpolarized.space_like import as3 from scipy import integrate +from large_n_limit import Agg_asymptotic, Aqq_asymptotic + XGRID = np.geomspace(1e-6, 1, 100) # 500 """X-grid.""" @@ -45,9 +47,15 @@ def integrand(u, x): if integrand == 0.0: return 0.0 + # compute the N space ome ome_n = compute_ome(nf, path.n, is_singlet) idx1, idx2 = MAP_ENTRIES[entry] ome_n = ome_n[idx1, idx2] + # subtract the large-N limit for diagonal terms (ie local and singular bits) + if entry in ["qq_ns", "qq"]: + ome_n -= Aqq_asymptotic(path.n, nf) + elif entry == "gg": + ome_n -= Agg_asymptotic(path.n, nf) # recombine everything return np.real(ome_n * integrand) @@ -82,8 +90,7 @@ def save_files(entry, ome_x, xgrid=XGRID): if __name__ == "__main__": # non diagonal temrms - for k in ["gq", "qg", "Hg", "Hq"]: + for k in ["qq_ns", "gg", "gq", "qg", "qq", "Hg", "Hq"]: # TODO: here we should use the lower patch nf, correct ?? result = [compute_xspace_ome(k, nf) for nf in [3, 4, 5]] save_files(k, result) - # ["ns", "gg", "qq",]: diff --git a/extras/ome_n3lo/largex_limit.py b/extras/ome_n3lo/large_n_limit.py similarity index 100% rename from extras/ome_n3lo/largex_limit.py rename to extras/ome_n3lo/large_n_limit.py diff --git a/extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb similarity index 91% rename from extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb rename to extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb index 51a05cd8e..31f89afb8 100644 --- a/extras/ome_n3lo/notebooks/Agg_Aqq_largex_expansion.nb +++ b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 41517, 1139] -NotebookOptionsPosition[ 38434, 1083] -NotebookOutlinePosition[ 38826, 1099] -CellTagsIndexPosition[ 38783, 1096] +NotebookDataLength[ 44215, 1218] +NotebookOptionsPosition[ 40619, 1155] +NotebookOutlinePosition[ 41011, 1171] +CellTagsIndexPosition[ 40968, 1168] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -969,8 +969,6 @@ Cell[BoxData[ "Out[271]=",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{ RowBox[{"(*", @@ -1039,6 +1037,8 @@ Cell[BoxData[ CellLabel-> "In[274]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"{", RowBox[{ @@ -1049,11 +1049,10 @@ Cell[BoxData[ RowBox[{"LG", "[", "N", "]"}]}], ",", RowBox[{ RowBox[{"-", "72.36717694258661`"}], "+", - RowBox[{"3.11448410587291`", " ", "NF"}]}]}], "}"}]], "Output", - CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { - 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.948953688166637*^9}, - CellLabel-> - "Out[274]=",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], + RowBox[{"3.11448410587291`", " ", "NF"}]}]}]}]], "Input", + CellChangeTimes->{{3.94895526412346*^9, + 3.9489552641239967`*^9}},ExpressionUUID->"5fe5ca95-25a2-4b98-8659-\ +62b0932393c1"], Cell[BoxData[ RowBox[{ @@ -1079,7 +1078,80 @@ Cell[BoxData[ Cell[BoxData[""], "Input", CellChangeTimes->{{3.94895127781951*^9, 3.9489512801199293`*^9}},ExpressionUUID->"783fabf2-705a-4b70-bf99-\ -6b0e4f5b0b1c"] +6b0e4f5b0b1c"], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{ + RowBox[{"ggasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"-", " ", + RowBox[{"(", + RowBox[{"aggQ3PLU", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], + RowBox[{"LG", "[", "N", "]"}]}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"ggasy", "[", + RowBox[{"[", "2", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"+", " ", + RowBox[{"(", + RowBox[{"aggQ3DEL", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], + " ", "//", " ", "Simplify"}]}], "Input", + CellChangeTimes->{{3.948955379166621*^9, 3.948955399860025*^9}}, + CellLabel-> + "In[282]:=",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", "669.1554507291286`"}], "+", + RowBox[{"41.84286985333757`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]], "Output", + CellChangeTimes->{3.948955511242378*^9}, + CellLabel-> + "Out[282]=",ExpressionUUID->"fecf1ce3-f280-4ff0-aaf4-d1f070df2ddf"], + +Cell[BoxData[ + RowBox[{"49.5041510989361`", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "14.442649813264895`"}], "+", + RowBox[{"1.`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]], "Output", + CellChangeTimes->{3.948955511245875*^9}, + CellLabel-> + "Out[283]=",ExpressionUUID->"9fa3cc0f-c485-4e1b-b7d3-c134806ba903"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"-", "565.4465327471261`"}], "+", + RowBox[{"28.65462637880661`", " ", "NF"}]}]], "Output", + CellChangeTimes->{3.948955511247541*^9}, + CellLabel-> + "Out[284]=",ExpressionUUID->"667a9454-d21c-48cb-a4b6-9925a27a04ae"], + +Cell[BoxData[ + RowBox[{"619.2420126046355`", "\[VeryThinSpace]", "-", + RowBox[{"17.52475977636971`", " ", "NF"}]}]], "Output", + CellChangeTimes->{3.9489555112496243`*^9}, + CellLabel-> + "Out[285]=",ExpressionUUID->"c19edfde-8d03-4857-97d7-b87ff1d81deb"] +}, Open ]] }, WindowSize->{1920, 964}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, @@ -1134,13 +1206,20 @@ Cell[CellGroupData[{ Cell[20176, 592, 12837, 332, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], Cell[33016, 926, 1469, 42, 51, "Output",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] }, Open ]], +Cell[34500, 971, 2350, 66, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], Cell[CellGroupData[{ -Cell[34522, 973, 2350, 66, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], -Cell[36875, 1041, 590, 14, 34, "Output",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], -Cell[37468, 1057, 434, 10, 34, "Output",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], -Cell[37905, 1069, 357, 6, 34, "Output",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] +Cell[36875, 1041, 486, 13, 30, "Input",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], +Cell[37364, 1056, 434, 10, 34, "Output",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], +Cell[37801, 1068, 357, 6, 34, "Output",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] }, Open ]], -Cell[38277, 1078, 153, 3, 30, "Input",ExpressionUUID->"783fabf2-705a-4b70-bf99-6b0e4f5b0b1c"] +Cell[38173, 1077, 153, 3, 30, "Input",ExpressionUUID->"783fabf2-705a-4b70-bf99-6b0e4f5b0b1c"], +Cell[CellGroupData[{ +Cell[38351, 1084, 1060, 31, 94, "Input",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], +Cell[39414, 1117, 331, 9, 34, "Output",ExpressionUUID->"fecf1ce3-f280-4ff0-aaf4-d1f070df2ddf"], +Cell[39748, 1128, 343, 9, 34, "Output",ExpressionUUID->"9fa3cc0f-c485-4e1b-b7d3-c134806ba903"], +Cell[40094, 1139, 251, 6, 34, "Output",ExpressionUUID->"667a9454-d21c-48cb-a4b6-9925a27a04ae"], +Cell[40348, 1147, 255, 5, 34, "Output",ExpressionUUID->"c19edfde-8d03-4857-97d7-b87ff1d81deb"] +}, Open ]] } ] *) From acaf4d87b484b77fd2399ca49ba91985ba1d16d2 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 13:33:56 +0100 Subject: [PATCH 05/18] expand docs --- extras/ome_n3lo/convert_ome_xspace.py | 5 +- extras/ome_n3lo/large_n_limit.py | 4 +- .../notebooks/Agg_Aqq_largeN_expansion.nb | 1201 +++++----- extras/ome_n3lo/notebooks/Xspace.m | 2128 ++++++++--------- 4 files changed, 1671 insertions(+), 1667 deletions(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index e127713bc..68f807c9b 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -1,3 +1,7 @@ +"""Dump a fast x-space grid of the N3LO transition matrix elements. +The output file have the structure: x_grid, nf=3, nf=4, nf=5. +""" + import numpy as np from click import progressbar from eko.mellin import Path @@ -91,6 +95,5 @@ def save_files(entry, ome_x, xgrid=XGRID): if __name__ == "__main__": # non diagonal temrms for k in ["qq_ns", "gg", "gq", "qg", "qq", "Hg", "Hq"]: - # TODO: here we should use the lower patch nf, correct ?? result = [compute_xspace_ome(k, nf) for nf in [3, 4, 5]] save_files(k, result) diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index b83a34fda..d398df5f7 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -1,6 +1,6 @@ -"""This file contains the large-N limit of the diagonal Matrix elements. +"""This file contains the large-N limit of the diagonal Matrix elements. -The expansions are obtained using the notebook Agg_Aqq_largex_expansion.nb. +The expansions are obtained using the notebook Agg_Aqq_largex_expansion.nb. We note that: * the limit og :math:`A_{qq}` is the same for non-singlet like and singlet-like expansions. diff --git a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb index 31f89afb8..10f64212b 100644 --- a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb +++ b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb @@ -1,5 +1,7 @@ (* Content-type: application/vnd.wolfram.mathematica *) + + (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) @@ -27,24 +29,24 @@ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ - RowBox[{"here", " ", "=", " ", - RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{"here", " ", "=", " ", + RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], - ";"}], "\n", + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + ";"}], "\n", RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}]}], "Code", CellChangeTimes->{{3.9489469906313868`*^9, 3.948946991034669*^9}, { - 3.948954007032343*^9, + 3.948954007032343*^9, 3.948954039800639*^9}},ExpressionUUID->"cf4d06e7-cd27-4f38-a624-\ 1bf2aace7b0c"], @@ -53,17 +55,17 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox["Sigma", - FontColor->RGBColor[1, 0, 0]], - RowBox[{" ", + FontColor->RGBColor[1, 0, 0]], + RowBox[{" ", RowBox[{ RowBox[{ - RowBox[{"-", " ", "A"}], " ", "summation", " ", "package", " ", "by", - " ", "Carsten", " ", "Schneider"}], " ", "\[LongDash]", " ", - RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", - RowBox[{"V", " ", "2.86", " ", - RowBox[{"(", + RowBox[{"-", " ", "A"}], " ", "summation", " ", "package", " ", "by", + " ", "Carsten", " ", "Schneider"}], " ", "\[LongDash]", " ", + RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", + RowBox[{"V", " ", "2.86", " ", + RowBox[{"(", RowBox[{ - RowBox[{"June", " ", "15"}], ",", " ", "2021"}], ")"}], " "}]}]}], + RowBox[{"June", " ", "15"}], ",", " ", "2021"}], ")"}], " "}]}]}], ButtonBox[ StyleBox["Help", "Hyperlink", FontVariations->{"Underline"->True}], @@ -82,13 +84,13 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"HarmonicSums", " ", "by", " ", "Jakob", " ", "Ablinger"}], " ", - "\[LongDash]", " ", - RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", - RowBox[{"Version", " ", "1.0"}]}], - RowBox[{"(", + RowBox[{"HarmonicSums", " ", "by", " ", "Jakob", " ", "Ablinger"}], " ", + "\[LongDash]", " ", + RowBox[{"\[Copyright]", " ", "RISC"}], " ", "\[LongDash]", " ", + RowBox[{"Version", " ", "1.0"}]}], + RowBox[{"(", RowBox[{ - RowBox[{"30", "/", "03"}], "/", "21"}], ")"}]}], + RowBox[{"30", "/", "03"}], "/", "21"}], ")"}]}], ButtonBox[ StyleBox["Help", "Hyperlink", FontVariations->{"Underline"->True}], @@ -106,100 +108,100 @@ Cell[BoxData[ Cell[BoxData[{ RowBox[{ - RowBox[{"here", " ", "=", " ", - RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\n", + RowBox[{"here", " ", "=", " ", + RowBox[{"NotebookDirectory", "[", "]"}]}], ";"}], "\n", RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], "\n", RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], - ";"}], "\n", + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], + ";"}], "\n", RowBox[{ RowBox[{ - RowBox[{"Get", "[", - RowBox[{"StringJoin", "[", - RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], - "\n"}], "\n", + RowBox[{"Get", "[", + RowBox[{"StringJoin", "[", + RowBox[{"here", ",", " ", "\"\\""}], "]"}], "]"}], ";"}], + "\n"}], "\n", RowBox[{ - RowBox[{"QCDConst", " ", "=", " ", - RowBox[{"{", + RowBox[{"QCDConst", " ", "=", " ", + RowBox[{"{", RowBox[{ - RowBox[{"CA", " ", "\[Rule]", " ", "3"}], ",", " ", - RowBox[{"TF", " ", "\[Rule]", " ", - RowBox[{"1", "/", "2"}]}], ",", " ", - RowBox[{"CF", " ", "\[Rule]", " ", - RowBox[{"4", "/", "3"}]}], ",", " ", - RowBox[{"B4", " ", "\[Rule]", " ", + RowBox[{"CA", " ", "\[Rule]", " ", "3"}], ",", " ", + RowBox[{"TF", " ", "\[Rule]", " ", + RowBox[{"1", "/", "2"}]}], ",", " ", + RowBox[{"CF", " ", "\[Rule]", " ", + RowBox[{"4", "/", "3"}]}], ",", " ", + RowBox[{"B4", " ", "\[Rule]", " ", RowBox[{ RowBox[{ - RowBox[{"-", "4"}], " ", "z2", " ", + RowBox[{"-", "4"}], " ", "z2", " ", RowBox[{ - RowBox[{"Log", "[", "2", "]"}], "^", "2"}]}], " ", "+", " ", + RowBox[{"Log", "[", "2", "]"}], "^", "2"}]}], " ", "+", " ", RowBox[{ - RowBox[{"2", "/", "3"}], " ", + RowBox[{"2", "/", "3"}], " ", RowBox[{ - RowBox[{"Log", "[", "2", "]"}], "^", "4"}]}], " ", "-", " ", + RowBox[{"Log", "[", "2", "]"}], "^", "4"}]}], " ", "-", " ", RowBox[{ - RowBox[{"13", "/", "2"}], " ", "z4"}], " ", "+", " ", + RowBox[{"13", "/", "2"}], " ", "z4"}], " ", "+", " ", RowBox[{"16", " ", "li4half"}]}]}]}], "}"}]}], ";"}]}], "Code", CellChangeTimes->{{3.948945446657963*^9, 3.948945479177684*^9}, { - 3.948945522327042*^9, 3.948945522782468*^9}, {3.9489482445131893`*^9, + 3.948945522327042*^9, 3.948945522782468*^9}, {3.9489482445131893`*^9, 3.948948271795343*^9}, {3.9489505412478857`*^9, 3.9489505417142143`*^9}, { - 3.9489510312362022`*^9, 3.948951079482356*^9}, {3.94895111925445*^9, + 3.9489510312362022`*^9, 3.948951079482356*^9}, {3.94895111925445*^9, 3.948951119583748*^9}}, CellLabel-> "In[217]:=",ExpressionUUID->"3e9423b7-e0d4-4093-b3ce-955024eadbb5"], Cell[BoxData[ RowBox[{ - RowBox[{"(*", " ", - RowBox[{"Matching", " ", "conditions", " ", "symbols"}], " ", "*)"}], - "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{"Matching", " ", "conditions", " ", "symbols"}], " ", "*)"}], + "\[IndentingNewLine]", RowBox[{ - RowBox[{"AggQ123N", ";"}], "\[IndentingNewLine]", - RowBox[{"AqqQPS3", ";"}], "\[IndentingNewLine]", + RowBox[{"AggQ123N", ";"}], "\[IndentingNewLine]", + RowBox[{"AqqQPS3", ";"}], "\[IndentingNewLine]", RowBox[{"AqqQNS123N", ";"}]}]}]], "Input", CellChangeTimes->{{3.9489455067904367`*^9, 3.94894552825358*^9}, { - 3.948950547119001*^9, + 3.948950547119001*^9, 3.948950561491927*^9}},ExpressionUUID->"38ac9fa3-fd03-4c80-97d5-\ f0a3587299c5"], Cell[BoxData[ RowBox[{ - RowBox[{"GetLargeXLimit", "[", - RowBox[{"expr_", ",", " ", "order_", ",", " ", "Log_"}], "]"}], " ", ":=", - " ", - RowBox[{"Module", "[", + RowBox[{"GetLargeXLimit", "[", + RowBox[{"expr_", ",", " ", "order_", ",", " ", "Log_"}], "]"}], " ", ":=", + " ", + RowBox[{"Module", "[", RowBox[{ - RowBox[{"{", "expansion", "}"}], ",", "\n", "\t", + RowBox[{"{", "expansion", "}"}], ",", "\n", "\t", RowBox[{ - RowBox[{"expansion", " ", "=", " ", - RowBox[{"SExpansion", "[", + RowBox[{"expansion", " ", "=", " ", + RowBox[{"SExpansion", "[", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"expr", " ", "/.", " ", + RowBox[{"expr", " ", "/.", " ", RowBox[{ RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "Log"}]}], " ", "/.", - " ", "QCDConst"}], " ", "//", " ", "ReduceToBasis"}], ",", " ", - "N", ",", " ", "order"}], "]"}]}], ";", "\n", "\t", - RowBox[{"{", + " ", "QCDConst"}], " ", "//", " ", "ReduceToBasis"}], ",", " ", + "N", ",", " ", "order"}], "]"}]}], ";", "\n", "\t", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"expansion", ",", - RowBox[{"LG", "[", "N", "]"}]}], "]"}], - RowBox[{"LG", "[", "N", "]"}]}], ",", " ", + RowBox[{"Coefficient", "[", + RowBox[{"expansion", ",", + RowBox[{"LG", "[", "N", "]"}]}], "]"}], + RowBox[{"LG", "[", "N", "]"}]}], ",", " ", RowBox[{ - RowBox[{"expansion", " ", "-", + RowBox[{"expansion", " ", "-", RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"expansion", ",", - RowBox[{"LG", "[", "N", "]"}]}], "]"}], - RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", "Simplify"}]}], + RowBox[{"Coefficient", "[", + RowBox[{"expansion", ",", + RowBox[{"LG", "[", "N", "]"}]}], "]"}], + RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", "Simplify"}]}], "}"}]}]}], "\n", "]"}]}]], "Code", CellChangeTimes->{{3.948948538528637*^9, 3.948948649446475*^9}, { 3.948948844433375*^9, 3.948949008788335*^9}}, @@ -210,123 +212,123 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"(*", + RowBox[{"(*", RowBox[{ RowBox[{ - "Some", " ", "checks", " ", "that", " ", "the", " ", "thing", " ", "is", + "Some", " ", "checks", " ", "that", " ", "the", " ", "thing", " ", "is", " ", "working", " ", "as", " ", "it", " ", "should"}], " ", "..."}], " ", - "*)"}], "\n", + "*)"}], "\n", RowBox[{ - RowBox[{"GetLargeXLimit", "[", + RowBox[{"GetLargeXLimit", "[", RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQPS3", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQPS3", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", "\n", - RowBox[{"GetLargeXLimit", "[", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", "\n", + RowBox[{"GetLargeXLimit", "[", RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", - RowBox[{"Coefficient", "[", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", + RowBox[{"Coefficient", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - RowBox[{"-", "1"}]}]}], " ", "/.", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], " ", "/.", " ", RowBox[{ - RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", - " ", "QCDConst"}], " ", "//", " ", "Expand"}], ",", - RowBox[{"S", "[", - RowBox[{"1", ",", "N"}], "]"}]}], "]"}], "\n", + RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", + " ", "QCDConst"}], " ", "//", " ", "Expand"}], ",", + RowBox[{"S", "[", + RowBox[{"1", ",", "N"}], "]"}]}], "]"}], "\n", RowBox[{ - RowBox[{"Series", "[", + RowBox[{"Series", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - RowBox[{"-", "1"}]}]}], "/.", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], "/.", " ", RowBox[{ - RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", - "QCDConst"}], ",", " ", - RowBox[{"{", - RowBox[{"N", ",", "Infinity", ",", "0"}], "}"}]}], " ", "]"}], "/.", - RowBox[{"{", + RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "0"}]}], " ", "/.", + "QCDConst"}], ",", " ", + RowBox[{"{", + RowBox[{"N", ",", "Infinity", ",", "0"}], "}"}]}], " ", "]"}], "/.", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"S", "[", - RowBox[{"2", ",", "N"}], "]"}], "\[Rule]", " ", "z2"}], ",", " ", + RowBox[{"S", "[", + RowBox[{"2", ",", "N"}], "]"}], "\[Rule]", " ", "z2"}], ",", " ", RowBox[{ - RowBox[{"S", "[", - RowBox[{"3", ",", "N"}], "]"}], "\[Rule]", " ", "z3"}]}], + RowBox[{"S", "[", + RowBox[{"3", ",", "N"}], "]"}], "\[Rule]", " ", "z3"}]}], "}"}]}]}]}]], "Code", CellChangeTimes->{{3.948949013421583*^9, 3.9489490753518457`*^9}, { - 3.948949822620695*^9, 3.948949849941022*^9}, {3.948950000521757*^9, + 3.948949822620695*^9, 3.948949849941022*^9}, {3.948950000521757*^9, 3.948950014801219*^9}}, CellLabel-> "In[223]:=",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { - 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9}, CellLabel-> "Out[223]=",ExpressionUUID->"932538e5-3fcc-4d6a-8839-992b3e2af928"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{ - RowBox[{"-", + RowBox[{"-", FractionBox[ - RowBox[{"448", " ", - RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ",", + RowBox[{"448", " ", + RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ",", RowBox[{ - FractionBox["1", "27"], " ", - RowBox[{"(", - RowBox[{"73", "+", - RowBox[{"80", " ", "z2"}], "-", + FractionBox["1", "27"], " ", + RowBox[{"(", + RowBox[{"73", "+", + RowBox[{"80", " ", "z2"}], "-", RowBox[{"48", " ", "z3"}]}], ")"}]}]}], "}"}]], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { - 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, 3.948950002023658*^9, 3.948951086434144*^9, 3.9489511458553877`*^9}, CellLabel-> "Out[224]=",ExpressionUUID->"0ccc496d-ebd3-4707-91cd-5192d14850da"], Cell[BoxData[ - RowBox[{"-", + RowBox[{"-", FractionBox["448", "81"]}]], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { - 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145856818*^9}, CellLabel-> "Out[225]=",ExpressionUUID->"580512ef-0d2c-49df-9693-7668a37ccce8"], @@ -341,35 +343,35 @@ In[223]:=",ExpressionUUID->"c498f812-14d3-4a68-9da2-c8e933e5afc4"], Cell[BoxData[ RowBox[{ RowBox[{ - RowBox[{"-", - FractionBox["448", "81"]}], " ", - RowBox[{"S", "[", - RowBox[{"1", ",", "N"}], "]"}]}], "+", - RowBox[{"(", + RowBox[{"-", + FractionBox["448", "81"]}], " ", + RowBox[{"S", "[", + RowBox[{"1", ",", "N"}], "]"}]}], "+", + RowBox[{"(", InterpretationBox[ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - FractionBox["73", "27"], "+", + FractionBox["73", "27"], "+", FractionBox[ - RowBox[{"80", " ", "z2"}], "27"], "-", + RowBox[{"80", " ", "z2"}], "27"], "-", FractionBox[ - RowBox[{"16", " ", "z3"}], "9"]}], ")"}], "+", + RowBox[{"16", " ", "z3"}], "9"]}], ")"}], "+", InterpretationBox[ SuperscriptBox[ - RowBox[{"O", "[", + RowBox[{"O", "[", FractionBox["1", "N"], "]"}], "1"], - SeriesData[N, + SeriesData[N, DirectedInfinity[1], {}, 0, 1, 1], Editable->False]}], - SeriesData[N, + SeriesData[N, DirectedInfinity[1], { - Rational[73, 27] + Rational[80, 27] $CellContext`z2 + + Rational[73, 27] + Rational[80, 27] $CellContext`z2 + Rational[-16, 9] $CellContext`z3}, 0, 1, 1], Editable->False], ")"}]}]], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { - 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, + 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, 3.948950002023658*^9, 3.948951086434144*^9, 3.948951146118248*^9}, CellLabel-> "Out[226]=",ExpressionUUID->"918f1b3f-684b-41b7-bb1e-09e8ac524de5"] @@ -379,31 +381,31 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"(*", " ", + RowBox[{"(*", " ", RowBox[{ - "Pure", " ", "singlet", " ", "term", " ", "is", " ", "convergent", " ", - "as", " ", "it", " ", "should"}], " ", "*)"}], "\n", - RowBox[{"SExpansion", "[", + "Pure", " ", "singlet", " ", "term", " ", "is", " ", "convergent", " ", + "as", " ", "it", " ", "should"}], " ", "*)"}], "\n", + RowBox[{"SExpansion", "[", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQPS3", ",", " ", "as", ",", " ", "3"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQPS3", ",", " ", "as", ",", " ", "3"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "->", " ", "1"}]}], - " ", "/.", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "->", " ", "1"}]}], + " ", "/.", " ", RowBox[{ - RowBox[{"L", "[", "M", "]"}], " ", "->", " ", "0"}]}], ",", " ", "N", + RowBox[{"L", "[", "M", "]"}], " ", "->", " ", "0"}]}], ",", " ", "N", ",", " ", "1"}], "]"}]}]], "Code", CellChangeTimes->{{3.948950247009811*^9, 3.948950270110826*^9}}, CellLabel-> "In[227]:=",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], Cell[BoxData["0"], "Output", - CellChangeTimes->{3.948950271429709*^9, 3.9489510906139727`*^9, + CellChangeTimes->{3.948950271429709*^9, 3.9489510906139727`*^9, 3.948951149651967*^9}, CellLabel-> "Out[227]=",ExpressionUUID->"d3bc2ff3-a6a1-4b6c-985e-9651a6d3b117"] @@ -413,19 +415,19 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"(*", " ", - RowBox[{"qqNS", " ", "asy"}], " ", "*)"}], "\n", - RowBox[{"qqNSasy", " ", "=", " ", - RowBox[{"GetLargeXLimit", "[", + RowBox[{"(*", " ", + RowBox[{"qqNS", " ", "asy"}], " ", "*)"}], "\n", + RowBox[{"qqNSasy", " ", "=", " ", + RowBox[{"GetLargeXLimit", "[", RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}]}]}]], "Code", CellChangeTimes->{{3.948950027207466*^9, 3.948950027437483*^9}, { 3.9489501048247967`*^9, 3.948950153621386*^9}, 3.948951106558529*^9}, @@ -433,59 +435,59 @@ Cell[BoxData[ "In[228]:=",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - FractionBox["141640", "2187"], "+", + FractionBox["141640", "2187"], "+", FractionBox[ - RowBox[{"1024", " ", "li4half"}], "27"], "+", + RowBox[{"1024", " ", "li4half"}], "27"], "+", FractionBox[ - RowBox[{"128", " ", - SuperscriptBox["ln2", "4"]}], "81"], "-", + RowBox[{"128", " ", + SuperscriptBox["ln2", "4"]}], "81"], "-", FractionBox[ - RowBox[{"24064", " ", "NF"}], "2187"], "+", + RowBox[{"24064", " ", "NF"}], "2187"], "+", FractionBox[ - RowBox[{"6592", " ", "z2"}], "81"], "-", + RowBox[{"6592", " ", "z2"}], "81"], "-", FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", + RowBox[{"256", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["z2", "2"]}], "15"], "-", + RowBox[{"256", " ", + SuperscriptBox["z2", "2"]}], "15"], "-", FractionBox[ - RowBox[{"280", " ", "z3"}], "27"], "+", + RowBox[{"280", " ", "z3"}], "27"], "+", FractionBox[ - RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", + RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", FractionBox[ - RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{"-", + RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"-", RowBox[{ - FractionBox["1", "3645"], - RowBox[{"2", " ", - RowBox[{"(", - RowBox[{"132700", "+", - RowBox[{"51840", " ", "li4half"}], "+", - RowBox[{"2160", " ", - SuperscriptBox["ln2", "4"]}], "-", - RowBox[{"11830", " ", "NF"}], "-", - RowBox[{"11760", " ", "z2"}], "-", - RowBox[{"12960", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "-", - RowBox[{"960", " ", "NF", " ", "z2"}], "+", - RowBox[{"6144", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"1152", " ", "NF", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"291105", " ", "z3"}], "+", - RowBox[{"3840", " ", "NF", " ", "z3"}], "-", - RowBox[{"107280", " ", "z2", " ", "z3"}], "-", - RowBox[{"166860", " ", "z4"}], "+", + FractionBox["1", "3645"], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"132700", "+", + RowBox[{"51840", " ", "li4half"}], "+", + RowBox[{"2160", " ", + SuperscriptBox["ln2", "4"]}], "-", + RowBox[{"11830", " ", "NF"}], "-", + RowBox[{"11760", " ", "z2"}], "-", + RowBox[{"12960", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "-", + RowBox[{"960", " ", "NF", " ", "z2"}], "+", + RowBox[{"6144", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"1152", " ", "NF", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"291105", " ", "z3"}], "+", + RowBox[{"3840", " ", "NF", " ", "z3"}], "-", + RowBox[{"107280", " ", "z2", " ", "z3"}], "-", + RowBox[{"166860", " ", "z4"}], "+", RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", - CellChangeTimes->{{3.9489500247139473`*^9, 3.948950039220125*^9}, - 3.948950111791774*^9, 3.948950157878325*^9, 3.94895110422303*^9, + CellChangeTimes->{{3.9489500247139473`*^9, 3.948950039220125*^9}, + 3.948950111791774*^9, 3.948950157878325*^9, 3.94895110422303*^9, 3.948951163201816*^9}, CellLabel-> "Out[228]=",ExpressionUUID->"14f874a8-730a-4bee-bb0b-f93be4c938f2"] @@ -495,27 +497,27 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"(*", " ", + RowBox[{"(*", " ", RowBox[{ - RowBox[{"qqNS", " ", "asy"}], ",", " ", - RowBox[{"for", " ", "singlet", " ", "like"}]}], " ", "*)"}], "\n", + RowBox[{"qqNS", " ", "asy"}], ",", " ", + RowBox[{"for", " ", "singlet", " ", "like"}]}], " ", "*)"}], "\n", RowBox[{ - RowBox[{"qqSasy", " ", "=", " ", - RowBox[{"GetLargeXLimit", "[", + RowBox[{"qqSasy", " ", "=", " ", + RowBox[{"GetLargeXLimit", "[", RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", - " ", + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", - RowBox[{"(*", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + RowBox[{"(*", " ", RowBox[{ - "check", " ", "that", " ", "the", " ", "2", " ", "are", " ", "the", " ", - "same"}], " ", "*)"}], "\n", + "check", " ", "that", " ", "the", " ", "2", " ", "are", " ", "the", " ", + "same"}], " ", "*)"}], "\n", RowBox[{"qqNSasy", " ", "-", " ", "qqSasy"}]}]}]], "Code", CellChangeTimes->{{3.9489500926863003`*^9, 3.9489501123045464`*^9}, { 3.948950162196804*^9, 3.948950206961136*^9}}, @@ -523,56 +525,56 @@ Cell[BoxData[ "In[231]:=",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - FractionBox["141640", "2187"], "+", + FractionBox["141640", "2187"], "+", FractionBox[ - RowBox[{"1024", " ", "li4half"}], "27"], "+", + RowBox[{"1024", " ", "li4half"}], "27"], "+", FractionBox[ - RowBox[{"128", " ", - SuperscriptBox["ln2", "4"]}], "81"], "-", + RowBox[{"128", " ", + SuperscriptBox["ln2", "4"]}], "81"], "-", FractionBox[ - RowBox[{"24064", " ", "NF"}], "2187"], "+", + RowBox[{"24064", " ", "NF"}], "2187"], "+", FractionBox[ - RowBox[{"6592", " ", "z2"}], "81"], "-", + RowBox[{"6592", " ", "z2"}], "81"], "-", FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", + RowBox[{"256", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["z2", "2"]}], "15"], "-", + RowBox[{"256", " ", + SuperscriptBox["z2", "2"]}], "15"], "-", FractionBox[ - RowBox[{"280", " ", "z3"}], "27"], "+", + RowBox[{"280", " ", "z3"}], "27"], "+", FractionBox[ - RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", + RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", FractionBox[ - RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{"-", + RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"-", RowBox[{ - FractionBox["1", "3645"], - RowBox[{"2", " ", - RowBox[{"(", - RowBox[{"132700", "+", - RowBox[{"51840", " ", "li4half"}], "+", - RowBox[{"2160", " ", - SuperscriptBox["ln2", "4"]}], "-", - RowBox[{"11830", " ", "NF"}], "-", - RowBox[{"11760", " ", "z2"}], "-", - RowBox[{"12960", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "-", - RowBox[{"960", " ", "NF", " ", "z2"}], "+", - RowBox[{"6144", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"1152", " ", "NF", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"291105", " ", "z3"}], "+", - RowBox[{"3840", " ", "NF", " ", "z3"}], "-", - RowBox[{"107280", " ", "z2", " ", "z3"}], "-", - RowBox[{"166860", " ", "z4"}], "+", + FractionBox["1", "3645"], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"132700", "+", + RowBox[{"51840", " ", "li4half"}], "+", + RowBox[{"2160", " ", + SuperscriptBox["ln2", "4"]}], "-", + RowBox[{"11830", " ", "NF"}], "-", + RowBox[{"11760", " ", "z2"}], "-", + RowBox[{"12960", " ", + SuperscriptBox["ln2", "2"], " ", "z2"}], "-", + RowBox[{"960", " ", "NF", " ", "z2"}], "+", + RowBox[{"6144", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"1152", " ", "NF", " ", + SuperscriptBox["z2", "2"]}], "+", + RowBox[{"291105", " ", "z3"}], "+", + RowBox[{"3840", " ", "NF", " ", "z3"}], "-", + RowBox[{"107280", " ", "z2", " ", "z3"}], "-", + RowBox[{"166860", " ", "z4"}], "+", RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { 3.948950204161031*^9, 3.948950211058175*^9}, 3.948951193419348*^9}, @@ -580,7 +582,7 @@ Cell[BoxData[ "Out[231]=",ExpressionUUID->"31a2b1bc-7efa-42df-bd24-d103791159cf"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]], "Output", CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { 3.948950204161031*^9, 3.948950211058175*^9}, 3.9489511934214067`*^9}, @@ -595,375 +597,375 @@ Cell[BoxData[ StyleBox[ RowBox[{ StyleBox[ - RowBox[{"(", "*"}]], " ", + RowBox[{"(", "*"}]], " ", RowBox[{ - RowBox[{"Gluon", " ", "Limit"}], ",", " ", + RowBox[{"Gluon", " ", "Limit"}], ",", " ", RowBox[{ - "aggQ3", " ", "expansion", " ", "is", " ", "added", " ", "later"}]}], - " ", + "aggQ3", " ", "expansion", " ", "is", " ", "added", " ", "later"}]}], + " ", StyleBox[ - RowBox[{"*", ")"}]]}], "Code"], - StyleBox["\n", "Code"], + RowBox[{"*", ")"}]]}], "Code"], + StyleBox["\n", "Code"], RowBox[{ RowBox[{ - StyleBox["ggasy", "Code"], - StyleBox[" ", "Code"], - StyleBox["=", "Code"], - StyleBox[" ", "Code"], + StyleBox["ggasy", "Code"], + StyleBox[" ", "Code"], + StyleBox["=", "Code"], + StyleBox[" ", "Code"], RowBox[{ - StyleBox["GetLargeXLimit", "Code"], "[", + StyleBox["GetLargeXLimit", "Code"], "[", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AggQ123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", - " ", - RowBox[{"aggQ3", " ", "\[Rule]", " ", "0"}]}], " ", "/.", " ", + RowBox[{"Coefficient", "[", + RowBox[{"AggQ123N", ",", " ", "as", ",", "3"}], "]"}], " ", "/.", + " ", + RowBox[{"aggQ3", " ", "\[Rule]", " ", "0"}]}], " ", "/.", " ", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", - RowBox[{"(*", " ", + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ - "Here", " ", "now", " ", "we", " ", "need", " ", "to", " ", "add", " ", - "also", " ", "the", " ", "aggQ3", " ", - RowBox[{"piece", ":", " ", "https", ":"}]}], "//", + "Here", " ", "now", " ", "we", " ", "need", " ", "to", " ", "add", " ", + "also", " ", "the", " ", "aggQ3", " ", + RowBox[{"piece", ":", " ", "https", ":"}]}], "//", RowBox[{ RowBox[{ - RowBox[{"arxiv", ".", "org"}], "/", "pdf"}], "/", "2211.05462"}]}], - ",", " ", - RowBox[{"see", " ", "ancillary", " ", "file", " ", - RowBox[{"Xspace", ".", "m"}]}]}], " ", "*)"}], "\n", - RowBox[{"(*", " ", - RowBox[{"Form", " ", "eq", " ", "4.6"}], " ", "*)"}], "\n", + RowBox[{"arxiv", ".", "org"}], "/", "pdf"}], "/", "2211.05462"}]}], + ",", " ", + RowBox[{"see", " ", "ancillary", " ", "file", " ", + RowBox[{"Xspace", ".", "m"}]}]}], " ", "*)"}], "\n", + RowBox[{"(*", " ", + RowBox[{"Form", " ", "eq", " ", "4.6"}], " ", "*)"}], "\n", RowBox[{ - RowBox[{"aggQ3DEL", " ", "=", " ", + RowBox[{"aggQ3DEL", " ", "=", " ", RowBox[{ - RowBox[{"Coefficient", "[", "\n", "\t\t", + RowBox[{"Coefficient", "[", "\n", "\t\t", RowBox[{ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - RowBox[{"CF", "*", - RowBox[{"TF", "^", "2"}], "*", - RowBox[{"(", + RowBox[{"CF", "*", + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"-", "1478"}], "/", "81"}], " ", "+", " ", - RowBox[{"NF", "*", - RowBox[{"(", + RowBox[{"-", "1478"}], "/", "81"}], " ", "+", " ", + RowBox[{"NF", "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"-", "1942"}], "/", "81"}], " ", "-", " ", + RowBox[{"-", "1942"}], "/", "81"}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"20", "*", "z2"}], ")"}], "/", "3"}]}], ")"}]}], - " ", "-", " ", + RowBox[{"(", + RowBox[{"20", "*", "z2"}], ")"}], "/", "3"}]}], ")"}]}], + " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"88", "*", "z2"}], ")"}], "/", "3"}], " ", "-", " ", - RowBox[{"7", "*", "z3"}]}], ")"}]}], " ", "+", " ", "\n", - " ", + RowBox[{"(", + RowBox[{"88", "*", "z2"}], ")"}], "/", "3"}], " ", "-", " ", + RowBox[{"7", "*", "z3"}]}], ")"}]}], " ", "+", " ", "\n", + " ", RowBox[{ - RowBox[{"(", - RowBox[{"64", "*", - RowBox[{"TF", "^", "3"}], "*", "z3"}], ")"}], "/", "27"}], " ", - "+", " ", + RowBox[{"(", + RowBox[{"64", "*", + RowBox[{"TF", "^", "3"}], "*", "z3"}], ")"}], "/", "27"}], " ", + "+", " ", RowBox[{ - RowBox[{"CF", "^", "2"}], "*", "TF", "*", - RowBox[{"(", + RowBox[{"CF", "^", "2"}], "*", "TF", "*", + RowBox[{"(", RowBox[{ - RowBox[{"274", "/", "9"}], " ", "+", " ", + RowBox[{"274", "/", "9"}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"95", "*", "z3"}], ")"}], "/", "3"}]}], ")"}]}], " ", - "+", " ", "\n", " ", - RowBox[{"CA", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"95", "*", "z3"}], ")"}], "/", "3"}]}], ")"}]}], " ", + "+", " ", "\n", " ", + RowBox[{"CA", "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"TF", "^", "2"}], "*", - RowBox[{"(", + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", RowBox[{ - RowBox[{"2587", "/", "135"}], " ", "+", " ", + RowBox[{"2587", "/", "135"}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"572", "*", "z2"}], ")"}], "/", "27"}], " ", "+", - " ", - RowBox[{"NF", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"572", "*", "z2"}], ")"}], "/", "27"}], " ", "+", + " ", + RowBox[{"NF", "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"-", "178"}], "/", "9"}], " ", "+", " ", + RowBox[{"-", "178"}], "/", "9"}], " ", "+", " ", RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{"196", "*", "z2"}], ")"}], "/", "27"}]}], ")"}]}], - " ", "-", " ", "\n", " ", + " ", "-", " ", "\n", " ", RowBox[{ - RowBox[{"(", - RowBox[{"291", "*", "z3"}], ")"}], "/", "10"}]}], ")"}]}], - " ", "+", " ", - RowBox[{"CF", "*", "TF", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"291", "*", "z3"}], ")"}], "/", "10"}]}], ")"}]}], + " ", "+", " ", + RowBox[{"CF", "*", "TF", "*", + RowBox[{"(", RowBox[{ - RowBox[{"16541", "/", "162"}], " ", "-", " ", + RowBox[{"16541", "/", "162"}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"64", "*", "B4"}], ")"}], "/", "3"}], " ", "+", - " ", - RowBox[{"52", "*", "z2"}], " ", "-", " ", + RowBox[{"(", + RowBox[{"64", "*", "B4"}], ")"}], "/", "3"}], " ", "+", + " ", + RowBox[{"52", "*", "z2"}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"2617", "*", "z3"}], ")"}], "/", "12"}], " ", "+", - " ", "\n", " ", + RowBox[{"(", + RowBox[{"2617", "*", "z3"}], ")"}], "/", "12"}], " ", "+", + " ", "\n", " ", RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{"128", "*", "z4"}], ")"}], "/", "3"}]}], ")"}]}]}], - ")"}]}], " ", "+", " ", + ")"}]}], " ", "+", " ", RowBox[{ - RowBox[{"CA", "^", "2"}], "*", "TF", "*", - RowBox[{"(", + RowBox[{"CA", "^", "2"}], "*", "TF", "*", + RowBox[{"(", RowBox[{ - RowBox[{"34315", "/", "324"}], " ", "+", " ", + RowBox[{"34315", "/", "324"}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"32", "*", "B4"}], ")"}], "/", "3"}], " ", "+", " ", + RowBox[{"(", + RowBox[{"32", "*", "B4"}], ")"}], "/", "3"}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"20435", "*", "z3"}], ")"}], "/", "216"}], " ", "+", - " ", "\n", " ", - RowBox[{"z2", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"20435", "*", "z3"}], ")"}], "/", "216"}], " ", "+", + " ", "\n", " ", + RowBox[{"z2", "*", + RowBox[{"(", RowBox[{ - RowBox[{"992", "/", "27"}], " ", "+", " ", - RowBox[{"24", "*", "z3"}]}], ")"}]}], " ", "-", " ", + RowBox[{"992", "/", "27"}], " ", "+", " ", + RowBox[{"24", "*", "z3"}]}], ")"}]}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"3778", "*", "z4"}], ")"}], "/", "27"}], " ", "-", - " ", + RowBox[{"(", + RowBox[{"3778", "*", "z4"}], ")"}], "/", "27"}], " ", "-", + " ", RowBox[{ - RowBox[{"(", - RowBox[{"304", "*", "z5"}], ")"}], "/", "9"}]}], ")"}]}]}], - ")"}], "*", - RowBox[{"Delta", "[", - RowBox[{"1", "-", "x"}], "]"}]}], ",", " ", "\n", " ", - RowBox[{"Delta", "[", - RowBox[{"1", "-", "x"}], "]"}], ",", " ", "1"}], "]"}], " ", "/.", - " ", "QCDConst"}]}], ";"}], "\n", - RowBox[{"(*", " ", - RowBox[{"Form", " ", "eq", " ", "4.7"}], " ", "*)"}], "\n", + RowBox[{"(", + RowBox[{"304", "*", "z5"}], ")"}], "/", "9"}]}], ")"}]}]}], + ")"}], "*", + RowBox[{"Delta", "[", + RowBox[{"1", "-", "x"}], "]"}]}], ",", " ", "\n", " ", + RowBox[{"Delta", "[", + RowBox[{"1", "-", "x"}], "]"}], ",", " ", "1"}], "]"}], " ", "/.", + " ", "QCDConst"}]}], ";"}], "\n", + RowBox[{"(*", " ", + RowBox[{"Form", " ", "eq", " ", "4.7"}], " ", "*)"}], "\n", RowBox[{ - RowBox[{"aggQ3PLU", " ", "=", " ", + RowBox[{"aggQ3PLU", " ", "=", " ", RowBox[{ - RowBox[{"Coefficient", "[", " ", "\n", "\t\t", + RowBox[{"Coefficient", "[", " ", "\n", "\t\t", RowBox[{ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"CA", "^", "2"}], "*", "TF", "*", - RowBox[{"(", + RowBox[{"CA", "^", "2"}], "*", "TF", "*", + RowBox[{"(", RowBox[{ - RowBox[{"32564", "/", - RowBox[{"(", - RowBox[{"729", "*", - RowBox[{"(", + RowBox[{"32564", "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], - " ", "+", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"32", "*", "B4"}], ")"}], "/", - RowBox[{"(", - RowBox[{"3", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"32", "*", "B4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"3", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], - " ", "+", " ", "\n", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", "\n", " ", RowBox[{ - RowBox[{"(", - RowBox[{"3248", "*", "z2"}], ")"}], "/", - RowBox[{"(", - RowBox[{"81", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"3248", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"81", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], - " ", "+", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"1796", "*", "z3"}], ")"}], "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"1796", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], - " ", "+", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], ")"}]}], + " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"104", "*", "z4"}], ")"}], "/", - RowBox[{"(", - RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}], " ", - "+", " ", "\n", " ", - RowBox[{"CA", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"104", "*", "z4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}], " ", + "+", " ", "\n", " ", + RowBox[{"CA", "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"TF", "^", "2"}], "*", - RowBox[{"(", + RowBox[{"TF", "^", "2"}], "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"-", "35168"}], "/", - RowBox[{"(", - RowBox[{"729", "*", - RowBox[{"(", + RowBox[{"-", "35168"}], "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"560", "*", "z2"}], ")"}], "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"560", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", "\n", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", "\n", " ", RowBox[{ - RowBox[{"(", - RowBox[{"1120", "*", "z3"}], ")"}], "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"1120", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "+", " ", - RowBox[{"NF", "*", - RowBox[{"(", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "+", " ", + RowBox[{"NF", "*", + RowBox[{"(", RowBox[{ RowBox[{ - RowBox[{"-", "55552"}], "/", - RowBox[{"(", - RowBox[{"729", "*", - RowBox[{"(", + RowBox[{"-", "55552"}], "/", + RowBox[{"(", + RowBox[{"729", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", "\n", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", "\n", " ", RowBox[{ - RowBox[{"(", - RowBox[{"160", "*", "z2"}], ")"}], "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"160", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "+", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"448", "*", "z3"}], ")"}], "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"448", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}]}], ")"}]}]}], ")"}]}], " ", "+", " ", "\n", - " ", - RowBox[{"CF", "*", "TF", "*", - RowBox[{"(", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}]}], ")"}]}]}], ")"}]}], " ", "+", " ", "\n", + " ", + RowBox[{"CF", "*", "TF", "*", + RowBox[{"(", RowBox[{ - RowBox[{"6152", "/", - RowBox[{"(", - RowBox[{"27", "*", - RowBox[{"(", + RowBox[{"6152", "/", + RowBox[{"(", + RowBox[{"27", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"64", "*", "B4"}], ")"}], "/", - RowBox[{"(", - RowBox[{"3", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"64", "*", "B4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"3", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"40", "*", "z2"}], ")"}], "/", - RowBox[{"(", - RowBox[{"1", " ", "-", " ", "x"}], ")"}]}], " ", "-", " ", - "\n", " ", + RowBox[{"(", + RowBox[{"40", "*", "z2"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}], " ", "-", " ", + "\n", " ", RowBox[{ - RowBox[{"(", - RowBox[{"1208", "*", "z3"}], ")"}], "/", - RowBox[{"(", - RowBox[{"9", "*", - RowBox[{"(", + RowBox[{"(", + RowBox[{"1208", "*", "z3"}], ")"}], "/", + RowBox[{"(", + RowBox[{"9", "*", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], - ")"}]}], " ", "-", " ", + RowBox[{"-", "1"}], " ", "+", " ", "x"}], ")"}]}], + ")"}]}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"96", "*", "z4"}], ")"}], "/", - RowBox[{"(", - RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}]}], - ")"}]}]}], " ", "//", "Simplify"}], "\n", " ", ",", " ", - RowBox[{"(", + RowBox[{"(", + RowBox[{"96", "*", "z4"}], ")"}], "/", + RowBox[{"(", + RowBox[{"1", " ", "-", " ", "x"}], ")"}]}]}], ")"}]}]}], + ")"}]}]}], " ", "//", "Simplify"}], "\n", " ", ",", " ", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1"}], "+", "x"}], ")"}], ",", - RowBox[{"-", "1"}]}], "]"}], " ", "/.", " ", "QCDConst"}]}], + RowBox[{"-", "1"}], "+", "x"}], ")"}], ",", + RowBox[{"-", "1"}]}], "]"}], " ", "/.", " ", "QCDConst"}]}], ";"}]}]}]], "Code", CellChangeTimes->{{3.948950055316721*^9, 3.948950063221066*^9}, { - 3.948950212826285*^9, 3.948950227872402*^9}, {3.948950356179121*^9, + 3.948950212826285*^9, 3.948950227872402*^9}, {3.948950356179121*^9, 3.948950383652822*^9}, {3.948950501756506*^9, 3.948950536228887*^9}, { - 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, + 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, 3.9489508160515337`*^9}, {3.948950869142365*^9, 3.948950905994871*^9}, { - 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, + 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, 3.9489536787425423`*^9}}, CellLabel-> "In[271]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - RowBox[{"-", - FractionBox["12820", "27"]}], "+", + RowBox[{"-", + FractionBox["12820", "27"]}], "+", FractionBox[ - RowBox[{"2624", " ", "NF"}], "81"], "-", + RowBox[{"2624", " ", "NF"}], "81"], "-", FractionBox[ - RowBox[{"556", " ", "z2"}], "9"], "+", + RowBox[{"556", " ", "z2"}], "9"], "+", FractionBox[ - RowBox[{"40", " ", "NF", " ", "z2"}], "9"], "-", - RowBox[{"24", " ", - SuperscriptBox["z2", "2"]}], "-", + RowBox[{"40", " ", "NF", " ", "z2"}], "9"], "-", + RowBox[{"24", " ", + SuperscriptBox["z2", "2"]}], "-", FractionBox[ - RowBox[{"208", " ", "z3"}], "9"], "+", + RowBox[{"208", " ", "z3"}], "9"], "+", FractionBox[ - RowBox[{"16", " ", "NF", " ", "z3"}], "9"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"16", " ", "NF", " ", "z3"}], "9"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", RowBox[{ - FractionBox["1", "27"], " ", - RowBox[{"(", + FractionBox["1", "27"], " ", + RowBox[{"(", RowBox[{ - RowBox[{"-", "12337"}], "+", - RowBox[{"9", " ", "NF", " ", - RowBox[{"(", - RowBox[{"58", "+", - RowBox[{"17", " ", "z2"}]}], ")"}]}], "+", - RowBox[{"88", " ", "z3"}], "-", - RowBox[{"3", " ", "z2", " ", - RowBox[{"(", - RowBox[{"137", "+", - RowBox[{"128", " ", "ln2"}], "+", + RowBox[{"-", "12337"}], "+", + RowBox[{"9", " ", "NF", " ", + RowBox[{"(", + RowBox[{"58", "+", + RowBox[{"17", " ", "z2"}]}], ")"}]}], "+", + RowBox[{"88", " ", "z3"}], "-", + RowBox[{"3", " ", "z2", " ", + RowBox[{"(", + RowBox[{"137", "+", + RowBox[{"128", " ", "ln2"}], "+", RowBox[{"324", " ", "z3"}]}], ")"}]}]}], ")"}]}]}], "}"}]], "Output",\ - CellChangeTimes->{{3.948950056566019*^9, 3.9489500690040627`*^9}, + CellChangeTimes->{{3.948950056566019*^9, 3.9489500690040627`*^9}, 3.948950232810248*^9, {3.948950736657477*^9, 3.948950820817873*^9}, { - 3.9489508804035892`*^9, 3.948950910733629*^9}, {3.948951248372204*^9, + 3.9489508804035892`*^9, 3.948950910733629*^9}, {3.948951248372204*^9, 3.9489512628739233`*^9}, 3.948953684019939*^9}, CellLabel-> "Out[271]=",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] @@ -971,68 +973,68 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{ - RowBox[{"(*", - RowBox[{"Get", " ", "the", " ", "numerical", " ", "values"}], " ", "*)"}], - "\n", + RowBox[{"(*", + RowBox[{"Get", " ", "the", " ", "numerical", " ", "values"}], " ", "*)"}], + "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"qqNSasy", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", - " ", "Simplify"}], "\n", "\n", - RowBox[{"(*", " ", + RowBox[{"qqNSasy", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], "\n", "\n", + RowBox[{"(*", " ", RowBox[{ RowBox[{ - RowBox[{"Here", " ", "we", " ", "have", " ", "that", " ", - RowBox[{"SExpansion", "[", " ", + RowBox[{"Here", " ", "we", " ", "have", " ", "that", " ", + RowBox[{"SExpansion", "[", " ", RowBox[{ - RowBox[{"Integrate", "[", + RowBox[{"Integrate", "[", RowBox[{ RowBox[{ - RowBox[{"1", "/", - RowBox[{"(", - RowBox[{"1", "-", "x"}], ")"}]}], - RowBox[{"(", + RowBox[{"1", "/", + RowBox[{"(", + RowBox[{"1", "-", "x"}], ")"}]}], + RowBox[{"(", RowBox[{ - RowBox[{"x", "^", - RowBox[{"(", - RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", - " ", - RowBox[{"{", - RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", - ",", "0"}], "]"}]}], " ", "\[Equal]", " ", - RowBox[{"-", " ", - RowBox[{"LG", "[", "N", "]"}]}]}], ",", " ", + RowBox[{"x", "^", + RowBox[{"(", + RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", + " ", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", + ",", "0"}], "]"}]}], " ", "\[Equal]", " ", + RowBox[{"-", " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ",", " ", RowBox[{ RowBox[{ "so", " ", "we", " ", "add", " ", "the", " ", "piece", " ", "with", " ", - "a"}], " ", "-", " ", - RowBox[{"sign", "!"}]}]}], " ", "*)"}], "\n", + "a"}], " ", "-", " ", + RowBox[{"sign", "!"}]}]}], " ", "*)"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", "-", " ", + RowBox[{"ggasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "-", " ", RowBox[{ - RowBox[{"(", - RowBox[{"aggQ3PLU", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}], - RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", - " ", "Simplify"}], "\n", + RowBox[{"(", + RowBox[{"aggQ3PLU", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}], + RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", "+", " ", - RowBox[{"(", - RowBox[{"aggQ3DEL", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], + RowBox[{"ggasy", "[", + RowBox[{"[", "2", "]"}], "]"}], " ", "+", " ", + RowBox[{"(", + RowBox[{"aggQ3DEL", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], " ", "//", " ", "Simplify"}]}]}]], "Code", CellChangeTimes->{{3.948951282360952*^9, 3.948951363262577*^9}, { - 3.9489533926644917`*^9, 3.9489534137431717`*^9}, {3.94895350090244*^9, + 3.9489533926644917`*^9, 3.9489534137431717`*^9}, {3.94895350090244*^9, 3.948953641550552*^9}}, CellLabel-> "In[274]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], @@ -1040,26 +1042,26 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"{", + RowBox[{"{", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{"20.36251906478134`", "\[VeryThinSpace]", "-", - RowBox[{"3.4050138869326796`", " ", "NF"}]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", + RowBox[{"(", + RowBox[{"20.36251906478134`", "\[VeryThinSpace]", "-", + RowBox[{"3.4050138869326796`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", RowBox[{ - RowBox[{"-", "72.36717694258661`"}], "+", + RowBox[{"-", "72.36717694258661`"}], "+", RowBox[{"3.11448410587291`", " ", "NF"}]}]}]}]], "Input", - CellChangeTimes->{{3.94895526412346*^9, + CellChangeTimes->{{3.94895526412346*^9, 3.9489552641239967`*^9}},ExpressionUUID->"5fe5ca95-25a2-4b98-8659-\ 62b0932393c1"], Cell[BoxData[ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - RowBox[{"-", "1384.1265693540154`"}], "+", - RowBox[{"91.34702095227367`", " ", "NF"}]}], ")"}], " ", + RowBox[{"-", "1384.1265693540154`"}], "+", + RowBox[{"91.34702095227367`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881680107`*^9}, @@ -1067,7 +1069,7 @@ Cell[BoxData[ "Out[275]=",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], Cell[BoxData[ - RowBox[{"53.795479857509356`", "\[VeryThinSpace]", "+", + RowBox[{"53.795479857509356`", "\[VeryThinSpace]", "+", RowBox[{"11.129866602436904`", " ", "NF"}]}]], "Output", CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881693697`*^9}, @@ -1076,7 +1078,7 @@ Cell[BoxData[ }, Open ]], Cell[BoxData[""], "Input", - CellChangeTimes->{{3.94895127781951*^9, + CellChangeTimes->{{3.94895127781951*^9, 3.9489512801199293`*^9}},ExpressionUUID->"783fabf2-705a-4b70-bf99-\ 6b0e4f5b0b1c"], @@ -1085,31 +1087,31 @@ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\[IndentingNewLine]", + RowBox[{"ggasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"-", " ", - RowBox[{"(", - RowBox[{"aggQ3PLU", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], - RowBox[{"LG", "[", "N", "]"}]}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\n", + RowBox[{"-", " ", + RowBox[{"(", + RowBox[{"aggQ3PLU", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], + RowBox[{"LG", "[", "N", "]"}]}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\n", RowBox[{ RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\[IndentingNewLine]", + RowBox[{"ggasy", "[", + RowBox[{"[", "2", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", + "Simplify"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ - RowBox[{"+", " ", - RowBox[{"(", - RowBox[{"aggQ3DEL", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], + RowBox[{"+", " ", + RowBox[{"(", + RowBox[{"aggQ3DEL", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], " ", "//", " ", "Simplify"}]}], "Input", CellChangeTimes->{{3.948955379166621*^9, 3.948955399860025*^9}}, CellLabel-> @@ -1117,21 +1119,21 @@ Cell[BoxData[{ Cell[BoxData[ RowBox[{ - RowBox[{"(", + RowBox[{"(", RowBox[{ - RowBox[{"-", "669.1554507291286`"}], "+", - RowBox[{"41.84286985333757`", " ", "NF"}]}], ")"}], " ", + RowBox[{"-", "669.1554507291286`"}], "+", + RowBox[{"41.84286985333757`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", CellChangeTimes->{3.948955511242378*^9}, CellLabel-> "Out[282]=",ExpressionUUID->"fecf1ce3-f280-4ff0-aaf4-d1f070df2ddf"], Cell[BoxData[ - RowBox[{"49.5041510989361`", " ", - RowBox[{"(", + RowBox[{"49.5041510989361`", " ", + RowBox[{"(", RowBox[{ - RowBox[{"-", "14.442649813264895`"}], "+", - RowBox[{"1.`", " ", "NF"}]}], ")"}], " ", + RowBox[{"-", "14.442649813264895`"}], "+", + RowBox[{"1.`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", CellChangeTimes->{3.948955511245875*^9}, CellLabel-> @@ -1139,14 +1141,14 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{ - RowBox[{"-", "565.4465327471261`"}], "+", + RowBox[{"-", "565.4465327471261`"}], "+", RowBox[{"28.65462637880661`", " ", "NF"}]}]], "Output", CellChangeTimes->{3.948955511247541*^9}, CellLabel-> "Out[284]=",ExpressionUUID->"667a9454-d21c-48cb-a4b6-9925a27a04ae"], Cell[BoxData[ - RowBox[{"619.2420126046355`", "\[VeryThinSpace]", "-", + RowBox[{"619.2420126046355`", "\[VeryThinSpace]", "-", RowBox[{"17.52475977636971`", " ", "NF"}]}]], "Output", CellChangeTimes->{3.9489555112496243`*^9}, CellLabel-> @@ -1223,4 +1225,3 @@ Cell[40348, 1147, 255, 5, 34, "Output",ExpressionUUID->"c19edfde-8d03-4857-97d7- } ] *) - diff --git a/extras/ome_n3lo/notebooks/Xspace.m b/extras/ome_n3lo/notebooks/Xspace.m index 7af32d1a1..7a8640677 100644 --- a/extras/ome_n3lo/notebooks/Xspace.m +++ b/extras/ome_n3lo/notebooks/Xspace.m @@ -1,1400 +1,1400 @@ -(* - Xspace.m - +(* + Xspace.m + ------------------------------------------------------------------------------------- - - "The Unpolarized and Polarized Single-Mass Three-Loop Heavy - Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$" - - Authors: J. Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, - A.~Goedicke, A.~von~Manteuffel, C.~Schneider, and K.~Sch\"onwald - - DESY 15-112 - - Any use of the code AGG requires to cite the above reference. - + + "The Unpolarized and Polarized Single-Mass Three-Loop Heavy + Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$" + + Authors: J. Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, + A.~Goedicke, A.~von~Manteuffel, C.~Schneider, and K.~Sch\"onwald + + DESY 15-112 + + Any use of the code AGG requires to cite the above reference. + ------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------- - - The x-space contributions to aggQ3 and \Delta aggQ3. - Delta and plus-contributions are identical in the unpolarized and polarized case. - - B4 = -4*z2*ln2^2+2/3*ln2^4-13/2*z4+16*li4fhalf - We use HarmonicSums notation. To interprete the expressions directly - one needs to use the mathematica package HarmonicSums. - + + The x-space contributions to aggQ3 and \Delta aggQ3. + Delta and plus-contributions are identical in the unpolarized and polarized case. + + B4 = -4*z2*ln2^2+2/3*ln2^4-13/2*z4+16*li4fhalf + We use HarmonicSums notation. To interprete the expressions directly + one needs to use the mathematica package HarmonicSums. + -------------------------------------------------------------------------------------*) - DEL = (CF*TF^2*(-1478/81 + NF*(-1942/81 - (20*z2)/3) - (88*z2)/3 - 7*z3) + - (64*TF^3*z3)/27 + CF^2*TF*(274/9 + (95*z3)/3) + - CA*(TF^2*(2587/135 + (572*z2)/27 + NF*(-178/9 + (196*z2)/27) - - (291*z3)/10) + CF*TF*(16541/162 - (64*B4)/3 + 52*z2 - (2617*z3)/12 + - (128*z4)/3)) + CA^2*TF*(34315/324 + (32*B4)/3 + (20435*z3)/216 + + DEL = (CF*TF^2*(-1478/81 + NF*(-1942/81 - (20*z2)/3) - (88*z2)/3 - 7*z3) + + (64*TF^3*z3)/27 + CF^2*TF*(274/9 + (95*z3)/3) + + CA*(TF^2*(2587/135 + (572*z2)/27 + NF*(-178/9 + (196*z2)/27) - + (291*z3)/10) + CF*TF*(16541/162 - (64*B4)/3 + 52*z2 - (2617*z3)/12 + + (128*z4)/3)) + CA^2*TF*(34315/324 + (32*B4)/3 + (20435*z3)/216 + z2*(992/27 + 24*z3) - (3778*z4)/27 - (304*z5)/9))*Delta[1-x]; - PLU = CA^2*TF*(32564/(729*(-1 + x)) + (32*B4)/(3*(-1 + x)) + - (3248*z2)/(81*(-1 + x)) + (1796*z3)/(27*(-1 + x)) + (104*z4)/(1 - x)) + - CA*(TF^2*(-35168/(729*(-1 + x)) - (560*z2)/(27*(-1 + x)) - - (1120*z3)/(27*(-1 + x)) + NF*(-55552/(729*(-1 + x)) - - (160*z2)/(27*(-1 + x)) + (448*z3)/(27*(-1 + x)))) + - CF*TF*(6152/(27*(-1 + x)) - (64*B4)/(3*(-1 + x)) - (40*z2)/(1 - x) - + PLU = CA^2*TF*(32564/(729*(-1 + x)) + (32*B4)/(3*(-1 + x)) + + (3248*z2)/(81*(-1 + x)) + (1796*z3)/(27*(-1 + x)) + (104*z4)/(1 - x)) + + CA*(TF^2*(-35168/(729*(-1 + x)) - (560*z2)/(27*(-1 + x)) - + (1120*z3)/(27*(-1 + x)) + NF*(-55552/(729*(-1 + x)) - + (160*z2)/(27*(-1 + x)) + (448*z3)/(27*(-1 + x)))) + + CF*TF*(6152/(27*(-1 + x)) - (64*B4)/(3*(-1 + x)) - (40*z2)/(1 - x) - (1208*z3)/(9*(-1 + x)) - (96*z4)/(1 - x))); - REGUNP = CF*TF^2*((-32*(587825 + 510903*x + 144333*x^2 + 466579*x^3 + 233280*x^4 + - 120960*x^5))/(127575*x) + (656*(1 + x)*z4)/9 - + REGUNP = CF*TF^2*((-32*(587825 + 510903*x + 144333*x^2 + 466579*x^3 + 233280*x^4 + + 120960*x^5))/(127575*x) + (656*(1 + x)*z4)/9 - (64*Sqrt[1 - x]*(-4853 - 134604*x - 15168*x^2 + 141920*x^3 + 26880*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(4725*x^(3/2)) - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(4725*x^(3/2)) - (64*Sqrt[1 - x]*(-4853 - 134604*x - 15168*x^2 + 141920*x^3 + 26880*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(4725*x^(3/2)) + - (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(45*x) + - (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) - - (64*(-366907 + 520277*x - 325024*x^2 - 436536*x^3 + 200160*x^4 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(4725*x^(3/2)) + + (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(45*x) + + (8192*(10 + 25*x + 4*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) - + (64*(-366907 + 520277*x - 325024*x^2 - 436536*x^3 + 200160*x^4 + 60480*x^5)*H[0, x])/42525 - (32*(-1925 - 28952*x + 8590*x^2)*H[0, x]^2)/ - 14175 + (8*(635 + 821*x + 80*x^2)*H[0, x]^3)/405 + - (28*(1 + x)*H[0, x]^4)/27 + - z3*((16*(1220 + 3455*x + 821*x^2 + 180*x^3))/(135*x) - - (224*(1 + x)*H[0, x])/9) + - ((-64*(-1 + x)*(32375 + 241607*x - 500920*x^2 - 175896*x^3 + 260640*x^4 + + 14175 + (8*(635 + 821*x + 80*x^2)*H[0, x]^3)/405 + + (28*(1 + x)*H[0, x]^4)/27 + + z3*((16*(1220 + 3455*x + 821*x^2 + 180*x^3))/(135*x) - + (224*(1 + x)*H[0, x])/9) + + ((-64*(-1 + x)*(32375 + 241607*x - 500920*x^2 - 175896*x^3 + 260640*x^4 + 60480*x^5))/(42525*x) - (64*(-1 + x)*(-32 + 85*x + 22*x^2)*H[0, x])/ - (81*x) + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + - ((-16*(-1 + x)*(-32 + 85*x + 22*x^2))/(81*x) - - (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 - - (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + - ((-64*(-5600 + 50750*x - 9352*x^2 + 2815*x^3))/(14175*x) - - (64*(-4 - 5*x - 5*x^2 + 8*x^3)*H[0, x])/(27*x) - + (81*x) + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + + ((-16*(-1 + x)*(-32 + 85*x + 22*x^2))/(81*x) - + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 - + (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + + ((-64*(-5600 + 50750*x - 9352*x^2 + 2815*x^3))/(14175*x) - + (64*(-4 - 5*x - 5*x^2 + 8*x^3)*H[0, x])/(27*x) - (64*(1 + x)*H[0, x]^2)/9 + (64*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/ - (9*x))*H[0, 1, x] - (64*(1 + x)*H[0, 1, x]^2)/3 + - z2*((-16*(21525 - 239225*x + 54733*x^2 + 8515*x^3))/(14175*x) - - (8*(455 - 43*x + 440*x^2)*H[0, x])/135 + (232*(1 + x)*H[0, x]^2)/9 - - (176*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + - (352*(1 + x)*H[0, 1, x])/9) + + (9*x))*H[0, 1, x] - (64*(1 + x)*H[0, 1, x]^2)/3 + + z2*((-16*(21525 - 239225*x + 54733*x^2 + 8515*x^3))/(14175*x) - + (8*(455 - 43*x + 440*x^2)*H[0, x])/135 + (232*(1 + x)*H[0, x]^2)/9 - + (176*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + + (352*(1 + x)*H[0, 1, x])/9) + ((256*(-5 + 20*x + 11*x^2 + 25*x^3))/(135*x) + (512*(1 + x)*H[0, x])/9)* - H[0, 0, 1, x] + ((-64*(-20 - 16*x + 11*x^2 + 22*x^3))/(27*x) + + H[0, 0, 1, x] + ((-64*(-20 - 16*x + 11*x^2 + 22*x^3))/(27*x) + (128*(1 + x)*H[0, x])/9)*H[0, 1, 1, x] - (1280*(1 + x)*H[0, 0, 0, 1, x])/ - 9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + (64*(1 + x)*H[0, 1, 1, 1, x])/9 + - NF*((-64*(-1 + x)*(1825 + 11671*x + 4579*x^2))/(729*x) + - (208*(1 + x)*z4)/9 + (64*(2846 + 2675*x + 332*x^2)*H[0, x])/243 - - (32*(-109 - 55*x + 68*x^2)*H[0, x]^2)/81 - - (16*(-31 - 61*x + 8*x^2)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + + 9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + (64*(1 + x)*H[0, 1, 1, 1, x])/9 + + NF*((-64*(-1 + x)*(1825 + 11671*x + 4579*x^2))/(729*x) + + (208*(1 + x)*z4)/9 + (64*(2846 + 2675*x + 332*x^2)*H[0, x])/243 - + (32*(-109 - 55*x + 68*x^2)*H[0, x]^2)/81 - + (16*(-31 - 61*x + 8*x^2)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + z3*((64*(-28 - 43*x - 4*x^2 + 18*x^3))/(27*x) - (640*(1 + x)*H[0, x])/ - 9) + ((128*(-1 + x)*(247 - 5*x + 166*x^2))/(243*x) - - (64*(-1 + x)*(14 + 113*x + 68*x^2)*H[0, x])/(81*x) - - (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + - ((-16*(-1 + x)*(152 + 197*x + 206*x^2))/(81*x) + - (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 + - (112*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + - ((-64*(14 + 271*x + 127*x^2 + 35*x^3))/(81*x) + - (128*(-2 + 11*x + 20*x^2 + 4*x^3)*H[0, x])/(27*x) + - (64*(1 + x)*H[0, x]^2)/9)*H[0, 1, x] + - z2*((16*(42 + 985*x + 553*x^2 + 208*x^3))/(81*x) - - (16*(25 + 37*x + 4*x^2)*H[0, x])/27 - (16*(1 + x)*H[0, x]^2)/9 - - (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + - (32*(1 + x)*H[0, 1, x])/9) + + 9) + ((128*(-1 + x)*(247 - 5*x + 166*x^2))/(243*x) - + (64*(-1 + x)*(14 + 113*x + 68*x^2)*H[0, x])/(81*x) - + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x]^2)/(27*x))*H[1, x] + + ((-16*(-1 + x)*(152 + 197*x + 206*x^2))/(81*x) + + (32*(-1 + x)*(4 + 7*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^2 + + (112*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^3)/(81*x) + + ((-64*(14 + 271*x + 127*x^2 + 35*x^3))/(81*x) + + (128*(-2 + 11*x + 20*x^2 + 4*x^3)*H[0, x])/(27*x) + + (64*(1 + x)*H[0, x]^2)/9)*H[0, 1, x] + + z2*((16*(42 + 985*x + 553*x^2 + 208*x^3))/(81*x) - + (16*(25 + 37*x + 4*x^2)*H[0, x])/27 - (16*(1 + x)*H[0, x]^2)/9 - + (16*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x])/(27*x) + + (32*(1 + x)*H[0, 1, x])/9) + ((-128*(-2 + 11*x + 20*x^2 + 4*x^3))/(27*x) - (128*(1 + x)*H[0, x])/9)* - H[0, 0, 1, x] + ((64*(4 + 50*x + 59*x^2 + 10*x^3))/(27*x) - - (128*(1 + x)*H[0, x])/9)*H[0, 1, 1, x] + - (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - - (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + - CA^2*TF*((32*B4*(-55 + 29*x + 3*x^2 + 5*x^3))/(15*x) + - (2*(136080 + 10390850*x - 25228915*x^2 + 41091867*x^3 - 35285580*x^4 - + H[0, 0, 1, x] + ((64*(4 + 50*x + 59*x^2 + 10*x^3))/(27*x) - + (128*(1 + x)*H[0, x])/9)*H[0, 1, 1, x] + + (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - + (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + + CA^2*TF*((32*B4*(-55 + 29*x + 3*x^2 + 5*x^3))/(15*x) + + (2*(136080 + 10390850*x - 25228915*x^2 + 41091867*x^3 - 35285580*x^4 - 2505916*x^5 + 16253784*x^6 - 4708800*x^7 + 103680*x^8))/ - (18225*(-1 + x)*x^2) - (1184*(1 + 3*x)*z5)/3 + + (18225*(-1 + x)*x^2) - (1184*(1 + 3*x)*z5)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - + ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - 468834*x^5 + 147720*x^6 - 2880*x^7 - 3600*Sqrt[1 - x]*x^(3/2)* Sqrt[-((-1 + x)*x)] + 7200*Sqrt[1 - x]*x^(5/2)*Sqrt[-((-1 + x)*x)]))/ (675*(-((-1 + x)*x))^(3/2)) - 3072*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, - x]) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + x]) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ - (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ - (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (15*x) + (1024*(-100 + 31*x + 6*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/ - (15*x) + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + - 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + - ((2*(-15120 + 329300*x + 1049115*x^2 - 2509187*x^3 + 2443924*x^4 + + (15*x) + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((2*(-15120 + 329300*x + 1049115*x^2 - 2509187*x^3 + 2443924*x^4 + 2516114*x^5 - 8557392*x^6 + 6400296*x^7 - 1719360*x^8 + 34560*x^9))/ - (2025*(-1 + x)*x^2) + (4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - + (2025*(-1 + x)*x^2) + (4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - 52837*x^4 - 3100*x^5 + 38183*x^6)*H[-1, x])/ - (405*(-1 + x)*x^2*(1 + x)) - - (8*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + - 142*x^7)*H[-1, x]^2)/(45*(-1 + x)^2*x^3) + + (405*(-1 + x)*x^2*(1 + x)) - + (8*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7)*H[-1, x]^2)/(45*(-1 + x)^2*x^3) + (16*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x]^3)/(27*x*(1 + x)))* - H[0, x] + ((-15120 - 225360*x + 502300*x^2 + 601385*x^3 - 1157959*x^4 - - 327521*x^5 + 757679*x^6 - 119204*x^7)/(2025*(-1 + x)^2*x^2*(1 + x)) - - (4*(-378 - 2874*x + 6011*x^2 - 475*x^3 - 4369*x^4 + 4433*x^5 - - 1324*x^6 + 56*x^7)*H[-1, x])/(135*(-1 + x)^2*x^3) + + H[0, x] + ((-15120 - 225360*x + 502300*x^2 + 601385*x^3 - 1157959*x^4 - + 327521*x^5 + 757679*x^6 - 119204*x^7)/(2025*(-1 + x)^2*x^2*(1 + x)) - + (4*(-378 - 2874*x + 6011*x^2 - 475*x^3 - 4369*x^4 + 4433*x^5 - + 1324*x^6 + 56*x^7)*H[-1, x])/(135*(-1 + x)^2*x^3) + (4*(10 + 146*x + 267*x^2 + 143*x^3 + 4*x^4)*H[-1, x]^2)/(9*x*(1 + x)))* - H[0, x]^2 + ((-8*(72 + 269*x + 97*x^2 + 110*x^3))/(81*x) - + H[0, x]^2 + ((-8*(72 + 269*x + 97*x^2 + 110*x^3))/(81*x) - (8*(-12 - 18*x - 19*x^2 - 24*x^3 + 5*x^4 + 12*x^5)*H[-1, x])/ (27*x^2*(1 + x)))*H[0, x]^3 - (2*(-20 + 41*x + 20*x^2 - 41*x^3 + 4*x^4)* - H[0, x]^4)/(27*(-1 + x)*(1 + x)) - (4*x*H[0, x]^5)/15 + + H[0, x]^4)/(27*(-1 + x)*(1 + x)) - (4*x*H[0, x]^5)/15 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* - ((-256*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 1536*(1 + x)*H[0, x]) + + ((-256*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 1536*(1 + x)*H[0, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* - ((-256*(180 - 167*x + 73*x^2 + 20*x^3))/(15*x) + 1536*(1 + x)*H[0, x]) + + ((-256*(180 - 167*x + 73*x^2 + 20*x^3))/(15*x) + 1536*(1 + x)*H[0, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - + ((-32*(-6720 + 71296*x - 133089*x^2 - 103314*x^3 + 495821*x^4 - 468834*x^5 + 147720*x^6 - 2880*x^7 - 3600*Sqrt[1 - x]*x^(3/2)* Sqrt[-((-1 + x)*x)] + 7200*Sqrt[1 - x]*x^(5/2)*Sqrt[-((-1 + x)*x)]))/ (675*(-((-1 + x)*x))^(3/2)) - 3072*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - ((-512*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 3072*(1 + x)*H[0, x])) + - ((2*(-45360 - 75530*x + 1565645*x^2 - 4951401*x^3 + 3302942*x^4 + - 11660542*x^5 - 25672176*x^6 + 19200888*x^7 - 5158080*x^8 + - 103680*x^9))/(6075*(-1 + x)*x^2) + - ((-2*(22014 - 8237*x - 114683*x^2 + 225135*x^3 - 153683*x^4 + - 42334*x^5))/(405*(-1 + x)*x^2) + + ((-512*(-4 - 21*x + 17*x^2 + 4*x^3))/(3*x) + 3072*(1 + x)*H[0, x])) + + ((2*(-45360 - 75530*x + 1565645*x^2 - 4951401*x^3 + 3302942*x^4 + + 11660542*x^5 - 25672176*x^6 + 19200888*x^7 - 5158080*x^8 + + 103680*x^9))/(6075*(-1 + x)*x^2) + + ((-2*(22014 - 8237*x - 114683*x^2 + 225135*x^3 - 153683*x^4 + + 42334*x^5))/(405*(-1 + x)*x^2) + (16*(-1 + x)*(-42 + 328*x + 267*x^2 + 294*x^3 + 122*x^4)*H[-1, x])/ - (45*x^3))*H[0, x] - (2*(252 - 2700*x - 4114*x^2 + 6895*x^3 + + (45*x^3))*H[0, x] - (2*(252 - 2700*x - 4114*x^2 + 6895*x^3 + 10437*x^4 - 6242*x^5 - 10300*x^6 - 3201*x^7 + 3725*x^8 + 2368*x^9)* - H[0, x]^2)/(135*(-1 + x)^2*x^3*(1 + x)^2) - + H[0, x]^2)/(135*(-1 + x)^2*x^3*(1 + x)^2) - (4*(24 + 4*x + 69*x^2 - 162*x^3 + 21*x^4 + 64*x^5)*H[0, x]^3)/ - (27*(-1 + x)*x^2))*H[1, x] + - ((-1536 + 3326*x - 1155*x^2 + 411*x^3 - 248*x^4)/(81*x^2) - + (27*(-1 + x)*x^2))*H[1, x] + + ((-1536 + 3326*x - 1155*x^2 + 411*x^3 - 248*x^4)/(81*x^2) - (2*(48 + 482*x + 601*x^2 - 199*x^3 - 863*x^4 - 127*x^5 + 82*x^6)* - H[0, x])/(27*x^2*(1 + x)^2) + + H[0, x])/(27*x^2*(1 + x)^2) + (2*(24 + 4*x + 29*x^2 - 93*x^3 + 58*x^4 + 30*x^5)*H[0, x]^2)/ (9*(-1 + x)*x^2))*H[1, x]^2 - (4*(16 - 31*x + 45*x^2 - 32*x^3 + 18*x^4)* - H[0, x]*H[1, x]^3)/(27*(-1 + x)*x) + - z4*((-2*(27640 - 13006*x - 80398*x^2 + 35703*x^3 + 75319*x^4 - 25548*x^5 - + H[0, x]*H[1, x]^3)/(27*(-1 + x)*x) + + z4*((-2*(27640 - 13006*x - 80398*x^2 + 35703*x^3 + 75319*x^4 - 25548*x^5 - 20424*x^6 + 4111*x^7 - 2377*x^8 + 2340*x^9))/ - (45*(-1 + x)^3*x*(1 + x)^3) + 32*(1 + x)*H[-1, x] - - (4*(69 + 113*x)*H[0, x])/3 + 28*(-1 + x)*H[1, x]) - - (32*(-370 - 27*x^2 + 122*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + - ((-4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - 52837*x^4 - 3100*x^5 + - 38183*x^6))/(405*(-1 + x)*x^2*(1 + x)) + - (16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + - 142*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - - (16*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + - ((8*(-378 - 2772*x + 3157*x^2 - 3904*x^3 + 9996*x^4 + 4058*x^5 - - 11795*x^6 + 4238*x^7 + 280*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - + (45*(-1 + x)^3*x*(1 + x)^3) + 32*(1 + x)*H[-1, x] - + (4*(69 + 113*x)*H[0, x])/3 + 28*(-1 + x)*H[1, x]) - + (32*(-370 - 27*x^2 + 122*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((-4*(-28659 - 46328*x + 50113*x^2 + 38308*x^3 - 52837*x^4 - 3100*x^5 + + 38183*x^6))/(405*(-1 + x)*x^2*(1 + x)) + + (16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - + (16*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + ((8*(-378 - 2772*x + 3157*x^2 - 3904*x^3 + 9996*x^4 + 4058*x^5 - + 11795*x^6 + 4238*x^7 + 280*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - (16*(12 + 44*x + 163*x^2 + 149*x^3 + 12*x^4)*H[-1, x])/(9*x^2))* - H[0, x] + (4*(120 + 1880*x - 3389*x^2 + 722*x^3 - 248*x^4 + 362*x^5 + + H[0, x] + (4*(120 + 1880*x - 3389*x^2 + 722*x^3 - 248*x^4 + 362*x^5 + 3917*x^6 - 2804*x^7 + 160*x^8)*H[0, x]^2)/(45*(-1 + x)^3*x^2* - (1 + x)) - (16*(-1 + x)*H[0, x]^3)/3 + - ((-16*(-1 + x)*(-42 + 328*x + 267*x^2 + 294*x^3 + 122*x^4))/(45*x^3) + - (32*(22 - 51*x^2 + 19*x^3 + 14*x^4)*H[0, x])/(9*(-1 + x)*x) - - 48*(-1 + x)*H[0, x]^2)*H[1, x])*H[0, -1, x] + - ((16*(6 + 95*x - 189*x^2 + 24*x^3 + 84*x^4 - 25*x^5 + 105*x^6 - 86*x^7 + - 10*x^8))/(9*(-1 + x)^3*x^2*(1 + x)) + (128*(-1 + x)*H[0, x])/3 - - 32*(-1 + x)*H[1, x])*H[0, -1, x]^2 + - ((-2*(125190 - 366745*x - 327315*x^2 + 1460740*x^3 - 437031*x^4 - + (1 + x)) - (16*(-1 + x)*H[0, x]^3)/3 + + ((-16*(-1 + x)*(-42 + 328*x + 267*x^2 + 294*x^3 + 122*x^4))/(45*x^3) + + (32*(22 - 51*x^2 + 19*x^3 + 14*x^4)*H[0, x])/(9*(-1 + x)*x) - + 48*(-1 + x)*H[0, x]^2)*H[1, x])*H[0, -1, x] + + ((16*(6 + 95*x - 189*x^2 + 24*x^3 + 84*x^4 - 25*x^5 + 105*x^6 - 86*x^7 + + 10*x^8))/(9*(-1 + x)^3*x^2*(1 + x)) + (128*(-1 + x)*H[0, x])/3 - + 32*(-1 + x)*H[1, x])*H[0, -1, x]^2 + + ((-2*(125190 - 366745*x - 327315*x^2 + 1460740*x^3 - 437031*x^4 - 1182779*x^5 + 637806*x^6 + 44234*x^7))/(2025*(-1 + x)^2*x^2* (1 + x)) + (16*(1 + x)*(-42 - 318*x + 277*x^2 + 146*x^3 + 52*x^4)* - H[-1, x])/(45*x^3) + (16*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x]^2)/(3*x) + - ((4*(252 - 3432*x + 1198*x^2 + 11292*x^3 - 11065*x^4 - 5263*x^5 + - 4433*x^6 - 5117*x^7 + 3382*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - + H[-1, x])/(45*x^3) + (16*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x]^2)/(3*x) + + ((4*(252 - 3432*x + 1198*x^2 + 11292*x^3 - 11065*x^4 - 5263*x^5 + + 4433*x^6 - 5117*x^7 + 3382*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) - (16*(-12 - 26*x - 75*x^2 - 60*x^3 + 4*x^4)*H[-1, x])/(9*x^2))* - H[0, x] + ((4*(24 - 184*x - 101*x^2 + 224*x^3 + 67*x^4 + 446*x^5 - + H[0, x] + ((4*(24 - 184*x - 101*x^2 + 224*x^3 + 67*x^4 + 446*x^5 - 57*x^6 - 828*x^7 - 235*x^8 + 342*x^9 + 110*x^10))/ - (9*(-1 + x)^3*x^2*(1 + x)^3) + 16*(1 + x)*H[-1, x])*H[0, x]^2 + - (40*(1 + x)*H[0, x]^3)/3 + - ((-4*(504 - 3456*x + 3508*x^2 + 13669*x^3 - 7102*x^4 - 17810*x^5 + - 4874*x^6 + 7057*x^7 + 556*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) - + (9*(-1 + x)^3*x^2*(1 + x)^3) + 16*(1 + x)*H[-1, x])*H[0, x]^2 + + (40*(1 + x)*H[0, x]^3)/3 + + ((-4*(504 - 3456*x + 3508*x^2 + 13669*x^3 - 7102*x^4 - 17810*x^5 + + 4874*x^6 + 7057*x^7 + 556*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) - (8*(24 + 28*x + 146*x^2 - 363*x^3 + 159*x^4 + 62*x^5)*H[0, x])/ - (9*(-1 + x)*x^2) + 16*(-1 + x)*H[0, x]^2)*H[1, x] - - (4*(20 + 60*x - 189*x^2 + 87*x^3 + 14*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + - ((16*(-380 + 558*x - 885*x^2 + 607*x^3 + 140*x^4))/(45*(-1 + x)*x) - - (64*(-1 + 11*x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + - ((8*(120 + 380*x - 553*x^2 - 1859*x^3 - 246*x^4 + 1516*x^5 + 1229*x^6 + - 363*x^7 + 90*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) - - 32*(1 + x)*H[-1, x] + (8*(5 + 41*x)*H[0, x])/3)*H[0, 1, x]^2 + - z3*((2*(-40222 + 34737*x + 214994*x^2 - 69552*x^3 - 305462*x^4 + - 27593*x^5 + 129250*x^6 + 22*x^7))/(135*(-1 + x)^2*x*(1 + x)^2) + - (8*(-480 - 120*x + 898*x^2 + 135*x^3 + 261*x^4 + 1930*x^5 - 876*x^6 - - 1085*x^7 + 437*x^8 + 340*x^9)*H[0, x])/(45*(-1 + x)^3*x*(1 + x)^3) + + (9*(-1 + x)*x^2) + 16*(-1 + x)*H[0, x]^2)*H[1, x] - + (4*(20 + 60*x - 189*x^2 + 87*x^3 + 14*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + + ((16*(-380 + 558*x - 885*x^2 + 607*x^3 + 140*x^4))/(45*(-1 + x)*x) - + (64*(-1 + 11*x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + + ((8*(120 + 380*x - 553*x^2 - 1859*x^3 - 246*x^4 + 1516*x^5 + 1229*x^6 + + 363*x^7 + 90*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) - + 32*(1 + x)*H[-1, x] + (8*(5 + 41*x)*H[0, x])/3)*H[0, 1, x]^2 + + z3*((2*(-40222 + 34737*x + 214994*x^2 - 69552*x^3 - 305462*x^4 + + 27593*x^5 + 129250*x^6 + 22*x^7))/(135*(-1 + x)^2*x*(1 + x)^2) + + (8*(-480 - 120*x + 898*x^2 + 135*x^3 + 261*x^4 + 1930*x^5 - 876*x^6 - + 1085*x^7 + 437*x^8 + 340*x^9)*H[0, x])/(45*(-1 + x)^3*x*(1 + x)^3) + 112*x*H[0, x]^2 + H[-1, x]* ((8*(12 + 58*x + 257*x^2 + 393*x^3 + 210*x^4 + 12*x^5))/ - (9*x^2*(1 + x)) - 32*(1 + x)*H[0, x]) + - ((8*(48 - 48*x + 41*x^2 + 18*x^3 - 83*x^4 + 44*x^5))/(9*(-1 + x)*x^2) - - 48*(-1 + x)*H[0, x])*H[1, x] - (16*(-17 + 5*x)*H[0, -1, x])/3 + - (32*(-8 + x)*H[0, 1, x])/3) + - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (9*x^2*(1 + x)) - 32*(1 + x)*H[0, x]) + + ((8*(48 - 48*x + 41*x^2 + 18*x^3 - 83*x^4 + 44*x^5))/(9*(-1 + x)*x^2) - + 48*(-1 + x)*H[0, x])*H[1, x] - (16*(-17 + 5*x)*H[0, -1, x])/3 + + (32*(-8 + x)*H[0, 1, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - ((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + + ((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + 96*x^6))/(45*(-1 + x)*x^3) + (512*(180 - 167*x + 73*x^2 + 20*x^3)* - H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + - (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - - 3072*(1 + x)*H[0, 1, x]) + - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, - x]*((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + + H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + + (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - + 3072*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + x]*((-128*(-168 + 1648*x - 4048*x^2 - 219*x^3 + 8023*x^4 - 5092*x^5 + 96*x^6))/(45*(-1 + x)*x^3) + (512*(180 - 167*x + 73*x^2 + 20*x^3)* - H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + - (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - - 3072*(1 + x)*H[0, 1, x]) + - ((-16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + - 142*x^7))/(45*(-1 + x)^2*x^3) + - (32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x])/(9*x*(1 + x)) - - (16*(24 + 210*x - 303*x^2 - 105*x^3 - 42*x^4 + 208*x^5 + 345*x^6 - - 297*x^7 + 8*x^8)*H[0, x])/(9*(-1 + x)^3*x^2*(1 + x)) - - 48*(-1 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, x]*H[1, x] - - (256*(-1 + x)*H[0, -1, x])/3 - 64*(-1 + x)*H[0, 1, x])*H[0, -1, -1, x] + - ((16*(42 - 380*x + 41*x^2 - 477*x^3 - 198*x^4 + 192*x^5))/(45*x^3) - - (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - + H[0, x])/(15*x) - 1536*(1 + x)*H[0, x]^2 + + (512*(-4 - 21*x + 17*x^2 + 4*x^3)*H[1, x])/(3*x) - + 3072*(1 + x)*H[0, 1, x]) + + ((-16*(42 + 376*x - 1063*x^2 + 315*x^3 + 1075*x^4 - 1013*x^5 + 6*x^6 + + 142*x^7))/(45*(-1 + x)^2*x^3) + + (32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4)*H[-1, x])/(9*x*(1 + x)) - + (16*(24 + 210*x - 303*x^2 - 105*x^3 - 42*x^4 + 208*x^5 + 345*x^6 - + 297*x^7 + 8*x^8)*H[0, x])/(9*(-1 + x)^3*x^2*(1 + x)) - + 48*(-1 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, x]*H[1, x] - + (256*(-1 + x)*H[0, -1, x])/3 - 64*(-1 + x)*H[0, 1, x])*H[0, -1, -1, x] + + ((16*(42 - 380*x + 41*x^2 - 477*x^3 - 198*x^4 + 192*x^5))/(45*x^3) - + (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - (16*(-60 - 450*x + 397*x^2 - 894*x^3 + 927*x^4 + 120*x^5)*H[0, x])/ (45*(-1 + x)*x^2) + 32*(-2 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, -1, x])* - H[0, -1, 1, x] + - ((-8*(-378 - 2292*x + 3177*x^2 - 13344*x^3 + 24836*x^4 + 8052*x^5 - - 26699*x^6 + 9744*x^7 + 504*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) + + H[0, -1, 1, x] + + ((-8*(-378 - 2292*x + 3177*x^2 - 13344*x^3 + 24836*x^4 + 8052*x^5 - + 26699*x^6 + 9744*x^7 + 504*x^8))/(135*(-1 + x)^2*x^3*(1 + x)) + (16*(24 + 102*x + 268*x^2 + 357*x^3 + 179*x^4 + 20*x^5)*H[-1, x])/ - (9*x^2*(1 + x)) + (16*(-60 - 1970*x + 3421*x^2 - 876*x^3 + 83*x^4 + + (9*x^2*(1 + x)) + (16*(-60 - 1970*x + 3421*x^2 - 876*x^3 + 83*x^4 + 377*x^5 - 4344*x^6 + 2409*x^7 + 120*x^8)*H[0, x])/ - (45*(-1 + x)^3*x^2*(1 + x)) + (80*(-2 + 5*x)*H[0, x]^2)/3 + - ((-64*(22 - 51*x^2 + 19*x^3 + 14*x^4))/(9*(-1 + x)*x) + - 224*(-1 + x)*H[0, x])*H[1, x] - (224*(-1 + x)*H[0, -1, x])/3 + - (160*(1 + 7*x)*H[0, 1, x])/3)*H[0, 0, -1, x] + - ((-4*(252 - 3660*x + 1086*x^2 + 23085*x^3 - 15078*x^4 - 37064*x^5 + + (45*(-1 + x)^3*x^2*(1 + x)) + (80*(-2 + 5*x)*H[0, x]^2)/3 + + ((-64*(22 - 51*x^2 + 19*x^3 + 14*x^4))/(9*(-1 + x)*x) + + 224*(-1 + x)*H[0, x])*H[1, x] - (224*(-1 + x)*H[0, -1, x])/3 + + (160*(1 + 7*x)*H[0, 1, x])/3)*H[0, 0, -1, x] + + ((-4*(252 - 3660*x + 1086*x^2 + 23085*x^3 - 15078*x^4 - 37064*x^5 + 11230*x^6 + 9173*x^7 - 7570*x^8 + 4146*x^9))/ - (135*(-1 + x)^2*x^3*(1 + x)^2) - - (16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4)*H[-1, x])/(9*x^2) + - ((-8*(120 - 1980*x - 1639*x^2 + 2720*x^3 + 3217*x^4 + 2980*x^5 - + (135*(-1 + x)^2*x^3*(1 + x)^2) - + (16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4)*H[-1, x])/(9*x^2) + + ((-8*(120 - 1980*x - 1639*x^2 + 2720*x^3 + 3217*x^4 + 2980*x^5 - 4117*x^6 - 8720*x^7 - 861*x^8 + 3560*x^9 + 880*x^10))/ - (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x])*H[0, x] - - (16*(23 + 21*x)*H[0, x]^2)/3 + + (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x])*H[0, x] - + (16*(23 + 21*x)*H[0, x]^2)/3 + ((16*(-12 + 66*x + 56*x^2 - 213*x^3 + 85*x^4 + 26*x^5))/ - (9*(-1 + x)*x^2) - 128*(-1 + x)*H[0, x])*H[1, x] + + (9*(-1 + x)*x^2) - 128*(-1 + x)*H[0, x])*H[1, x] + (32*(-5 + 17*x)*H[0, -1, x])/3 - (64*(2 + 17*x)*H[0, 1, x])/3)* H[0, 0, 1, x] + ((-16*(1 + x)*(-42 - 318*x + 277*x^2 + 146*x^3 + 52*x^4))/ - (45*x^3) - (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - + (45*x^3) - (32*(1 + x)*(6 + 7*x + 6*x^2)*H[-1, x])/(3*x) - (16*(-60 - 450*x + 313*x^2 - 810*x^3 + 927*x^4 + 120*x^5)*H[0, x])/ - (45*(-1 + x)*x^2) + 32*(-2 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, -1, x] + - 64*(1 + x)*H[0, 1, x])*H[0, 1, -1, x] + - ((8*(504 - 3576*x + 2523*x^2 + 12509*x^3 - 6137*x^4 - 15000*x^5 + - 4229*x^6 + 6247*x^7 + 501*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) + - (128*(1 + x)^3*H[-1, x])/(9*x) + - ((8*(24 + 152*x + 640*x^2 + 517*x^3 - 872*x^4 - 902*x^5 + 248*x^6 + - 433*x^7 + 64*x^8))/(9*(-1 + x)*x^2*(1 + x)^3) + - 64*(1 + x)*H[-1, x])*H[0, x] - (64*(-1 + 2*x)*H[0, x]^2)/3 + + (45*(-1 + x)*x^2) + 32*(-2 + x)*H[0, x]^2 + 64*(-1 + x)*H[0, -1, x] + + 64*(1 + x)*H[0, 1, x])*H[0, 1, -1, x] + + ((8*(504 - 3576*x + 2523*x^2 + 12509*x^3 - 6137*x^4 - 15000*x^5 + + 4229*x^6 + 6247*x^7 + 501*x^8))/(135*(-1 + x)*x^3*(1 + x)^2) + + (128*(1 + x)^3*H[-1, x])/(9*x) + + ((8*(24 + 152*x + 640*x^2 + 517*x^3 - 872*x^4 - 902*x^5 + 248*x^6 + + 433*x^7 + 64*x^8))/(9*(-1 + x)*x^2*(1 + x)^3) + + 64*(1 + x)*H[-1, x])*H[0, x] - (64*(-1 + 2*x)*H[0, x]^2)/3 + (16*(-4 + 16*x - 2*x^2 - 31*x^3 + 15*x^4 + 4*x^5)*H[1, x])/ - (3*(-1 + x)*x^2) + (176*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + - z2*((2*(15120 + 75320*x + 61440*x^2 - 157300*x^3 + 100449*x^4 - + (3*(-1 + x)*x^2) + (176*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + + z2*((2*(15120 + 75320*x + 61440*x^2 - 157300*x^3 + 100449*x^4 - 169674*x^5 - 289559*x^6 + 318304*x^7))/(2025*(-1 + x)^2*x^2* - (1 + x)) - (16*(4 + x)*z3)/3 + - (16*(-42 - 341*x + 850*x^2 - 715*x^3 - 117*x^4 + 1086*x^5 - 721*x^6 + - 60*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - - (8*(24 + 119*x + 183*x^2 + 118*x^3 + 22*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + - ((-4*(-488 - 718*x - 1075*x^2 + 1830*x^3 + 3714*x^4 - 1714*x^5 - - 2151*x^6 + 314*x^7))/(27*(-1 + x)^2*x*(1 + x)^2) + + (1 + x)) - (16*(4 + x)*z3)/3 + + (16*(-42 - 341*x + 850*x^2 - 715*x^3 - 117*x^4 + 1086*x^5 - 721*x^6 + + 60*x^7)*H[-1, x])/(45*(-1 + x)^2*x^3) - + (8*(24 + 119*x + 183*x^2 + 118*x^3 + 22*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + ((-4*(-488 - 718*x - 1075*x^2 + 1830*x^3 + 3714*x^4 - 1714*x^5 - + 2151*x^6 + 314*x^7))/(27*(-1 + x)^2*x*(1 + x)^2) + (8*(-12 + 46*x + 137*x^2 + 165*x^3 + 142*x^4 + 68*x^5)*H[-1, x])/ - (9*x^2*(1 + x)))*H[0, x] + - ((-4*(15 - 68*x - 75*x^2 + 202*x^3 + 243*x^4 - 200*x^5 - 105*x^6 + + (9*x^2*(1 + x)))*H[0, x] + + ((-4*(15 - 68*x - 75*x^2 + 202*x^3 + 243*x^4 - 200*x^5 - 105*x^6 + 66*x^7 + 18*x^8))/(9*(-1 + x)^3*(1 + x)^3) + 8*(1 + x)*H[-1, x])* - H[0, x]^2 + 8*(1 + x)*H[0, x]^3 + - ((8*(130 + 1261*x + 1069*x^2 - 2361*x^3 - 2613*x^4 + 1229*x^5 + - 1444*x^6 + 141*x^7))/(45*(-1 + x)*x^2*(1 + x)^2) + + H[0, x]^2 + 8*(1 + x)*H[0, x]^3 + + ((8*(130 + 1261*x + 1069*x^2 - 2361*x^3 - 2613*x^4 + 1229*x^5 + + 1444*x^6 + 141*x^7))/(45*(-1 + x)*x^2*(1 + x)^2) + (16*(30 - 47*x + 118*x^2 - 195*x^3 + 85*x^4 + 25*x^5)*H[0, x])/ - (9*(-1 + x)*x^2) + 8*(-1 + x)*H[0, x]^2)*H[1, x] + - (4*(12 + 19*x - 90*x^2 + 47*x^3 + 4*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + - ((-8*(60 + 1090*x - 2702*x^2 + 2241*x^3 - 634*x^4 - 1834*x^5 + - 3876*x^6 - 1977*x^7 + 120*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) + - (32*(-5 + 2*x)*H[0, x])/3 + 32*(-1 + x)*H[1, x])*H[0, -1, x] + - ((-8*(300 - 310*x - 1888*x^2 - 2639*x^3 - 2446*x^4 + 656*x^5 + - 4604*x^6 + 3053*x^7 + 430*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) + - 32*(1 + x)*H[-1, x] - (32*(5 + 8*x)*H[0, x])/3)*H[0, 1, x] + - (64*(-1 + x)*H[0, -1, -1, x])/3 - 64*x*H[0, -1, 1, x] - - (16*(-13 + 43*x)*H[0, 0, -1, x])/3 + (32*(12 + 17*x)*H[0, 0, 1, x])/3 - - 64*x*H[0, 1, -1, x] - (80*(1 + x)*H[0, 1, 1, x])/3) + - ((-32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4))/(9*x*(1 + x)) + - (256*(-1 + x)*H[0, x])/3)*H[0, -1, -1, -1, x] + + (9*(-1 + x)*x^2) + 8*(-1 + x)*H[0, x]^2)*H[1, x] + + (4*(12 + 19*x - 90*x^2 + 47*x^3 + 4*x^4)*H[1, x]^2)/(9*(-1 + x)*x) + + ((-8*(60 + 1090*x - 2702*x^2 + 2241*x^3 - 634*x^4 - 1834*x^5 + + 3876*x^6 - 1977*x^7 + 120*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) + + (32*(-5 + 2*x)*H[0, x])/3 + 32*(-1 + x)*H[1, x])*H[0, -1, x] + + ((-8*(300 - 310*x - 1888*x^2 - 2639*x^3 - 2446*x^4 + 656*x^5 + + 4604*x^6 + 3053*x^7 + 430*x^8))/(45*(-1 + x)*x^2*(1 + x)^3) + + 32*(1 + x)*H[-1, x] - (32*(5 + 8*x)*H[0, x])/3)*H[0, 1, x] + + (64*(-1 + x)*H[0, -1, -1, x])/3 - 64*x*H[0, -1, 1, x] - + (16*(-13 + 43*x)*H[0, 0, -1, x])/3 + (32*(12 + 17*x)*H[0, 0, 1, x])/3 - + 64*x*H[0, 1, -1, x] - (80*(1 + x)*H[0, 1, 1, x])/3) + + ((-32*(12 - 5*x - 27*x^2 - 4*x^3 + 14*x^4))/(9*x*(1 + x)) + + (256*(-1 + x)*H[0, x])/3)*H[0, -1, -1, -1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - 64*(-1 + x)*H[0, x])* - H[0, -1, -1, 1, x] + + H[0, -1, -1, 1, x] + ((-16*(60 + 440*x + 776*x^2 - 605*x^3 - 1066*x^4 + 225*x^5 + 250*x^6))/ (45*(-1 + x)*x^2*(1 + x)) + (32*(3 + 17*x)*H[0, x])/3)* - H[0, -1, 0, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - - 64*(-1 + x)*H[0, x])*H[0, -1, 1, -1, x] + - ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, -1, 1, 1, x] + + H[0, -1, 0, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - + 64*(-1 + x)*H[0, x])*H[0, -1, 1, -1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, -1, 1, 1, x] + ((-16*(24 + 102*x + 268*x^2 + 357*x^3 + 179*x^4 + 20*x^5))/ - (9*x^2*(1 + x)) - (64*(-5 + 8*x)*H[0, x])/3)*H[0, 0, -1, -1, x] + - ((16*(120 + 350*x + 927*x^2 + 945*x^3 + 50*x^4))/(45*x^2) + - (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + - ((-8*(-120 - 6000*x + 10349*x^2 - 3180*x^3 + 134*x^4 + 2788*x^5 - - 14283*x^6 + 6352*x^7 + 1080*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) - - (32*(1 + 64*x)*H[0, x])/3 - 384*(-1 + x)*H[1, x])*H[0, 0, 0, -1, x] + - ((8*(120 - 3040*x - 3262*x^2 + 3305*x^3 + 7136*x^4 + 5735*x^5 - 8426*x^6 - + (9*x^2*(1 + x)) - (64*(-5 + 8*x)*H[0, x])/3)*H[0, 0, -1, -1, x] + + ((16*(120 + 350*x + 927*x^2 + 945*x^3 + 50*x^4))/(45*x^2) + + (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + + ((-8*(-120 - 6000*x + 10349*x^2 - 3180*x^3 + 134*x^4 + 2788*x^5 - + 14283*x^6 + 6352*x^7 + 1080*x^8))/(45*(-1 + x)^3*x^2*(1 + x)) - + (32*(1 + 64*x)*H[0, x])/3 - 384*(-1 + x)*H[1, x])*H[0, 0, 0, -1, x] + + ((8*(120 - 3040*x - 3262*x^2 + 3305*x^3 + 7136*x^4 + 5735*x^5 - 8426*x^6 - 17625*x^7 - 748*x^8 + 6825*x^9 + 1340*x^10))/ - (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x] + - 16*(35 + 27*x)*H[0, x] + 288*(-1 + x)*H[1, x])*H[0, 0, 0, 1, x] + - ((16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4))/(9*x^2) + - (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + + (45*(-1 + x)^3*x^2*(1 + x)^3) - 32*(1 + x)*H[-1, x] + + 16*(35 + 27*x)*H[0, x] + 288*(-1 + x)*H[1, x])*H[0, 0, 0, 1, x] + + ((16*(24 + 70*x + 219*x^2 + 189*x^3 + 10*x^4))/(9*x^2) + + (128*(5 + 8*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + ((-16*(60 + 890*x - 236*x^2 - 2031*x^3 - 64*x^4 + 1271*x^5 + 290*x^6))/ (45*(-1 + x)*x^2*(1 + x)) - (176*(5 + 3*x)*H[0, x])/3)* - H[0, 0, 1, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - - 64*(-1 + x)*H[0, x])*H[0, 1, -1, -1, x] + - ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, -1, 1, x] + - ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, 1, -1, x] + + H[0, 0, 1, 1, x] + ((32*(1 + x)*(6 + 7*x + 6*x^2))/(3*x) - + 64*(-1 + x)*H[0, x])*H[0, 1, -1, -1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, -1, 1, x] + + ((-128*(1 + x)^3)/(9*x) - 64*(1 + x)*H[0, x])*H[0, 1, 1, -1, x] + ((-8*(-72 + 220*x - 201*x^2 - 12*x^3 + 25*x^4 + 20*x^5))/ - (9*(-1 + x)*x^2) + (32*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] + - (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 + - (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + - 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] + - (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + - (32*(-17 + 23*x)*H[0, 0, -1, 0, -1, x])/3 - - (32*(-9 + 55*x)*H[0, 0, -1, 0, 1, x])/3 + - 128*(1 + x)*H[0, 0, -1, 1, 1, x] + 32*(-17 + 23*x)*H[0, 0, 0, -1, -1, x] - - 32*(11 + 45*x)*H[0, 0, 0, -1, 1, x] + - (64*(26 + 59*x)*H[0, 0, 0, 0, -1, x])/3 - - (16*(213 + 137*x)*H[0, 0, 0, 0, 1, x])/3 - - 32*(11 + 45*x)*H[0, 0, 0, 1, -1, x] + 80*(11 + 21*x)*H[0, 0, 0, 1, 1, x] - - (64*(6 + 23*x)*H[0, 0, 1, 0, -1, x])/3 + - (32*(21 + 68*x)*H[0, 0, 1, 0, 1, x])/3 - - 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - - 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + - CF^2*TF*((64*B4*(-150 + 29*x + 38*x^2))/(15*x) - - (8*(5040 - 206320*x - 48375*x^2 + 145681*x^3 + 224786*x^4 - 242592*x^5 + - 56800*x^6))/(675*x^2) - (32*(5 + 137*x)*z5)/3 + + (9*(-1 + x)*x^2) + (32*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] + + (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 + + (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] + + (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + + (32*(-17 + 23*x)*H[0, 0, -1, 0, -1, x])/3 - + (32*(-9 + 55*x)*H[0, 0, -1, 0, 1, x])/3 + + 128*(1 + x)*H[0, 0, -1, 1, 1, x] + 32*(-17 + 23*x)*H[0, 0, 0, -1, -1, x] - + 32*(11 + 45*x)*H[0, 0, 0, -1, 1, x] + + (64*(26 + 59*x)*H[0, 0, 0, 0, -1, x])/3 - + (16*(213 + 137*x)*H[0, 0, 0, 0, 1, x])/3 - + 32*(11 + 45*x)*H[0, 0, 0, 1, -1, x] + 80*(11 + 21*x)*H[0, 0, 0, 1, 1, x] - + (64*(6 + 23*x)*H[0, 0, 1, 0, -1, x])/3 + + (32*(21 + 68*x)*H[0, 0, 1, 0, 1, x])/3 - + 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + + CF^2*TF*((64*B4*(-150 + 29*x + 38*x^2))/(15*x) - + (8*(5040 - 206320*x - 48375*x^2 + 145681*x^3 + 224786*x^4 - 242592*x^5 + + 56800*x^6))/(675*x^2) - (32*(5 + 137*x)*z5)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* ((-512*Sqrt[1 - x]*(-1680 + 16064*x + 17227*x^2 - 47376*x^3 + 14640*x^4))/ - (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - 4096*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x]) + - (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(15*x) + - (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x]) + + (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(15*x) + + (4096*(-150 - 57*x + 38*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ (15*x) + (4096*(-150 - 57*x + 38*x^2)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), (1 - VarGL)^(-1)}, x])/(15*x) + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), (1 - VarGL)^(-1)}, x])/(15*x) + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + 12288*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + - ((-4*(-10080 + 78560*x + 401475*x^2 - 895353*x^3 - 673372*x^4 + - 2713024*x^5 - 1984224*x^6 + 413760*x^7))/(675*x^2) - - (32*(1 + x)*(-3442 + 3169*x + 233*x^2)*H[-1, x])/(135*x^2) - + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((-4*(-10080 + 78560*x + 401475*x^2 - 895353*x^3 - 673372*x^4 + + 2713024*x^5 - 1984224*x^6 + 413760*x^7))/(675*x^2) - + (32*(1 + x)*(-3442 + 3169*x + 233*x^2)*H[-1, x])/(135*x^2) - (16*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4)*H[-1, x]^2)/ - (45*x^3) + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^3)/(9*x))*H[0, x] + - ((4*(-5040 - 93360*x + 204810*x^2 + 1735*x^3 + 7512*x^4))/(675*x^2) + + (45*x^3) + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^3)/(9*x))*H[0, x] + + ((4*(-5040 - 93360*x + 204810*x^2 + 1735*x^3 + 7512*x^4))/(675*x^2) + (8*(1 + x)*(252 + 2208*x - 5236*x^2 + 675*x^3 + 164*x^4)*H[-1, x])/ - (45*x^3) - (160*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(9*x))*H[0, x]^2 + + (45*x^3) - (160*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(9*x))*H[0, x]^2 + ((-2*(41 + 553*x + 8*x^2))/27 - (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/ - (27*x))*H[0, x]^3 - (4*(-3 - 3*x + 4*x^2)*H[0, x]^4)/27 + - (2*(1 + x)*H[0, x]^5)/15 + + (27*x))*H[0, x]^3 - (4*(-3 - 3*x + 4*x^2)*H[0, x]^4)/27 + + (2*(1 + x)*H[0, x]^5)/15 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* - (-3072*(-1 + x) + 2048*(1 + x)*H[0, x]) + + (-3072*(-1 + x) + 2048*(1 + x)*H[0, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* - ((1024*(-300 - 69*x + 31*x^2))/(15*x) + 2048*(1 + x)*H[0, x]) + - z4*((4*(63880 - 6891*x - 273*x^2 + 4140*x^3))/(45*x) - - (16*(61 + 109*x)*H[0, x])/3) + + ((1024*(-300 - 69*x + 31*x^2))/(15*x) + 2048*(1 + x)*H[0, x]) + + z4*((4*(63880 - 6891*x - 273*x^2 + 4140*x^3))/(45*x) - + (16*(61 + 109*x)*H[0, x])/3) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* ((-512*Sqrt[1 - x]*(-1680 + 16064*x + 17227*x^2 - 47376*x^3 + 14640*x^4))/ - (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1)}, x] + + (675*x^(3/2)) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1)}, x] + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - (-6144*(-1 + x) + 4096*(1 + x)*H[0, x])) + - ((-16*(-1 + x)*(2520 + 61125*x - 100200*x^2 + 117297*x^3 + 285640*x^4 - - 392616*x^5 + 103440*x^6))/(675*x^2) + - ((16*(-1 + x)*(-6380 + 7348*x + 9085*x^2 + 1260*x^3))/(135*x^2) + + (-6144*(-1 + x) + 4096*(1 + x)*H[0, x])) + + ((-16*(-1 + x)*(2520 + 61125*x - 100200*x^2 + 117297*x^3 + 285640*x^4 - + 392616*x^5 + 103440*x^6))/(675*x^2) + + ((16*(-1 + x)*(-6380 + 7348*x + 9085*x^2 + 1260*x^3))/(135*x^2) + (64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3)*H[-1, x])/(45*x^3))* H[0, x] + (4*(-1 + x)*(168 - 1472*x - 3312*x^2 - 747*x^3 + 308*x^4)* H[0, x]^2)/(45*x^3) - (16*(-1 + x)*(8 + 23*x + 8*x^2)*H[0, x]^3)/ - (27*x))*H[1, x] + ((-8*(-1 + x)*(-6 - 80*x + 89*x^2))/(9*x) + + (27*x))*H[1, x] + ((-8*(-1 + x)*(-6 - 80*x + 89*x^2))/(9*x) + (8*(-1 + x)*(-8 + 33*x + 16*x^2)*H[0, x])/(9*x) + 8*(-1 + x)*H[0, x]^2)* - H[1, x]^2 + ((-4*(-1 + x)*(-20 + 17*x + 52*x^2))/(27*x) - - (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^3 - - (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) - - (128*(-410 + 429*x^2)*H[0, x]*H[-1, 1, x])/(45*x^2) + - ((32*(1 + x)*(-3442 + 3169*x + 233*x^2))/(135*x^2) + + H[1, x]^2 + ((-4*(-1 + x)*(-20 + 17*x + 52*x^2))/(27*x) - + (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(27*x))*H[1, x]^3 - + (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) - + (128*(-410 + 429*x^2)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((32*(1 + x)*(-3442 + 3169*x + 233*x^2))/(135*x^2) + (32*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4)*H[-1, x])/ - (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(3*x) + + (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/(3*x) + ((16*(-252 - 2460*x + 3028*x^2 + 5201*x^3 - 539*x^4 + 164*x^5))/ - (45*x^3) + (512*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] + - (16*(-2680 + 1062*x - 747*x^2 + 120*x^3)*H[0, x]^2)/(45*x) - - (64*(-1 + x)*H[0, x]^3)/9 + - ((-64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) + - (128*(-1 + x)*(1 + 4*x + x^2)*H[0, x])/(3*x))*H[1, x])*H[0, -1, x] + + (45*x^3) + (512*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] + + (16*(-2680 + 1062*x - 747*x^2 + 120*x^3)*H[0, x]^2)/(45*x) - + (64*(-1 + x)*H[0, x]^3)/9 + + ((-64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) + + (128*(-1 + x)*(1 + 4*x + x^2)*H[0, x])/(3*x))*H[1, x])*H[0, -1, x] + ((32*(-182 + 48*x - 21*x^2 + 10*x^3))/(9*x) + (256*(-1 + x)*H[0, x])/3)* - H[0, -1, x]^2 + - ((-16*(34420 - 91980*x - 112215*x^2 + 67150*x^3 + 15519*x^4))/(675*x^2) - - (64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3)*H[-1, x])/(45*x^3) + - ((-16*(-84 + 820*x + 920*x^2 - 1680*x^3 + 3365*x^4 + 74*x^5))/(45*x^3) - - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x))*H[0, x] + - (16*(172 + 45*x + 54*x^2 + 8*x^3)*H[0, x]^2)/(9*x) + - (32*(1 + x)*H[0, x]^3)/3 + + H[0, -1, x]^2 + + ((-16*(34420 - 91980*x - 112215*x^2 + 67150*x^3 + 15519*x^4))/(675*x^2) - + (64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3)*H[-1, x])/(45*x^3) + + ((-16*(-84 + 820*x + 920*x^2 - 1680*x^3 + 3365*x^4 + 74*x^5))/(45*x^3) - + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x))*H[0, x] + + (16*(172 + 45*x + 54*x^2 + 8*x^3)*H[0, x]^2)/(9*x) + + (32*(1 + x)*H[0, x]^3)/3 + ((16*(168 - 1640*x - 2368*x^2 + 5431*x^3 - 1511*x^4 + 40*x^5))/ - (45*x^3) + (32*(-1 + x)*(4 - 11*x + 4*x^2)*H[0, x])/(3*x))*H[1, x] + - (16*(-1 + x)*(4 - 11*x + 4*x^2)*H[1, x]^2)/(9*x) + + (45*x^3) + (32*(-1 + x)*(4 - 11*x + 4*x^2)*H[0, x])/(3*x))*H[1, x] + + (16*(-1 + x)*(4 - 11*x + 4*x^2)*H[1, x]^2)/(9*x) + ((128*(145 + 71*x + 61*x^2 + 5*x^3))/(15*x) - 128*(1 + x)*H[0, x])* - H[0, -1, x])*H[0, 1, x] + + H[0, -1, x])*H[0, 1, x] + ((16*(-1860 + 3*x - 147*x^2 + 80*x^3))/(45*x) + 32*(1 + x)*H[0, x])* - H[0, 1, x]^2 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + H[0, 1, x]^2 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - ((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - - (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + - 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, - x]*((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - - (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + - 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + - z3*((4*(-70004 + 3299*x - 4455*x^2 + 3368*x^3))/(45*x) - - (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/x + - (16*(390 - 663*x + 140*x^2)*H[0, x])/45 + (8*(-15 + x)*H[0, x]^2)/3 - - (16*(-1 + x)*(8 - 13*x + 8*x^2)*H[1, x])/(9*x) - - 192*(-1 + x)*H[0, -1, x] - (32*(1 + x)*H[0, 1, x])/3) + - ((-32*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4))/(45*x^3) + - (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - - (64*(-58 + 8*x - 15*x^2 + 6*x^3)*H[0, x])/(3*x) - - (320*(-1 + x)*H[0, x]^2)/3 - 256*(-1 + x)*H[0, -1, x])*H[0, -1, -1, x] + - ((64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) - - (256*(70 - 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, -1, 1, x] + + ((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - + (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + + 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + x]*((1024*(-84 + 820*x - 477*x^2 - 3108*x^3 + 1204*x^4))/(45*x^3) - + (2048*(-300 - 69*x + 31*x^2)*H[0, x])/(15*x) - 2048*(1 + x)*H[0, x]^2 + + 6144*(-1 + x)*H[1, x] - 4096*(1 + x)*H[0, 1, x]) + + z3*((4*(-70004 + 3299*x - 4455*x^2 + 3368*x^3))/(45*x) - + (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/x + + (16*(390 - 663*x + 140*x^2)*H[0, x])/45 + (8*(-15 + x)*H[0, x]^2)/3 - + (16*(-1 + x)*(8 - 13*x + 8*x^2)*H[1, x])/(9*x) - + 192*(-1 + x)*H[0, -1, x] - (32*(1 + x)*H[0, 1, x])/3) + + ((-32*(1 + x)*(84 + 736*x - 1736*x^2 - 439*x^3 + 164*x^4))/(45*x^3) + + (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - + (64*(-58 + 8*x - 15*x^2 + 6*x^3)*H[0, x])/(3*x) - + (320*(-1 + x)*H[0, x]^2)/3 - 256*(-1 + x)*H[0, -1, x])*H[0, -1, -1, x] + + ((64*(-1 + x)*(-42 + 368*x + 875*x^2 + 446*x^3))/(45*x^3) - + (256*(70 - 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, -1, 1, x] + ((-16*(-252 - 2460*x + 3028*x^2 + 5841*x^3 - 239*x^4 + 492*x^5))/ - (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - - (64*(-2690 + 1338*x - 717*x^2 + 70*x^3)*H[0, x])/(45*x) + + (45*x^3) - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) - + (64*(-2690 + 1338*x - 717*x^2 + 70*x^3)*H[0, x])/(45*x) + (256*(-2 + 3*x)*H[0, x]^2)/3 - (256*(-1 + x)*(1 + 4*x + x^2)*H[1, x])/ (3*x) - 128*(-1 + x)*H[0, -1, x] + 256*(1 + x)*H[0, 1, x])* - H[0, 0, -1, x] + + H[0, 0, -1, x] + ((8*(-168 + 1640*x + 1840*x^2 - 4215*x^3 + 16165*x^4 + 228*x^5))/ - (45*x^3) + (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) + - (32*(-1760 - 507*x - 90*x^2 + 80*x^3)*H[0, x])/(45*x) - + (45*x^3) + (256*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(3*x) + + (32*(-1760 - 507*x - 90*x^2 + 80*x^3)*H[0, x])/(45*x) - (16*(23 + 31*x)*H[0, x]^2)/3 - (32*(-1 + x)*(8 - 25*x + 8*x^2)*H[1, x])/ (3*x) + 256*(-1 + x)*H[0, -1, x] - (448*(1 + x)*H[0, 1, x])/3)* - H[0, 0, 1, x] + ((64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3))/(45*x^3) - - (256*(70 + 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, 1, -1, x] + + H[0, 0, 1, x] + ((64*(1 + x)*(42 + 368*x - 875*x^2 + 446*x^3))/(45*x^3) - + (256*(70 + 43*x + 38*x^2)*H[0, x])/(15*x))*H[0, 1, -1, x] + ((-32*(168 - 1640*x - 2348*x^2 + 5381*x^3 - 1551*x^4 + 145*x^5))/ - (45*x^3) - (128*(-6 + 24*x - 12*x^2 + 7*x^3)*H[0, x])/(9*x) - + (45*x^3) - (128*(-6 + 24*x - 12*x^2 + 7*x^3)*H[0, x])/(9*x) - (32*(1 + x)*H[0, x]^2)/3 - (32*(-1 + x)*(4 - 47*x + 4*x^2)*H[1, x])/ - (9*x) + (64*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + - z2*((4*(3360 - 31980*x - 136015*x^2 + 34035*x^3 + 14992*x^4))/(225*x^2) - - 16*(5 + 13*x)*z3 - (16*(1 + x)*(168 + 1472*x - 3486*x^2 + 453*x^3 + + (9*x) + (64*(1 + x)*H[0, 1, x])/3)*H[0, 1, 1, x] + + z2*((4*(3360 - 31980*x - 136015*x^2 + 34035*x^3 + 14992*x^4))/(225*x^2) - + 16*(5 + 13*x)*z3 - (16*(1 + x)*(168 + 1472*x - 3486*x^2 + 453*x^3 + 164*x^4)*H[-1, x])/(45*x^3) + (64*(1 + x)*(1 - 4*x + x^2)*H[-1, x]^2)/ - (3*x) + ((-2*(61 + 437*x + 144*x^2))/3 + - (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] - - (8*(-1 + 25*x + 4*x^2)*H[0, x]^2)/3 + (4*(1 + x)*H[0, x]^3)/9 + - ((-4*(-1316 + 8217*x - 8157*x^2 + 1736*x^3))/(45*x) - - (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(9*x))*H[1, x] - - (4*(-1 + x)*(20 + 23*x + 20*x^2)*H[1, x]^2)/(3*x) + - ((-32*(-1780 + 666*x - 471*x^2 + 80*x^3))/(45*x) + - (128*(-1 + x)*H[0, x])/3)*H[0, -1, x] + + (3*x) + ((-2*(61 + 437*x + 144*x^2))/3 + + (128*(1 + x)*(1 - 4*x + x^2)*H[-1, x])/(9*x))*H[0, x] - + (8*(-1 + 25*x + 4*x^2)*H[0, x]^2)/3 + (4*(1 + x)*H[0, x]^3)/9 + + ((-4*(-1316 + 8217*x - 8157*x^2 + 1736*x^3))/(45*x) - + (16*(-1 + x)*(4 + 25*x + 4*x^2)*H[0, x])/(9*x))*H[1, x] - + (4*(-1 + x)*(20 + 23*x + 20*x^2)*H[1, x]^2)/(3*x) + + ((-32*(-1780 + 666*x - 471*x^2 + 80*x^3))/(45*x) + + (128*(-1 + x)*H[0, x])/3)*H[0, -1, x] + ((-8*(40 + 1611*x + 1041*x^2 + 260*x^3))/(45*x) + 32*(1 + x)*H[0, x])* - H[0, 1, x] + 128*(-1 + x)*H[0, -1, -1, x] - - 128*(-2 + 3*x)*H[0, 0, -1, x] + (32*(1 + 13*x)*H[0, 0, 1, x])/3 + - (176*(1 + x)*H[0, 1, 1, x])/3) + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + - 256*(-1 + x)*H[0, x])*H[0, -1, -1, -1, x] + - ((-256*(71 + 5*x^2))/15 + 256*H[0, x])*H[0, -1, 0, 1, x] + + H[0, 1, x] + 128*(-1 + x)*H[0, -1, -1, x] - + 128*(-2 + 3*x)*H[0, 0, -1, x] + (32*(1 + 13*x)*H[0, 0, 1, x])/3 + + (176*(1 + x)*H[0, 1, 1, x])/3) + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + + 256*(-1 + x)*H[0, x])*H[0, -1, -1, -1, x] + + ((-256*(71 + 5*x^2))/15 + 256*H[0, x])*H[0, -1, 0, 1, x] + ((128*(1 + x)*(1 - 4*x + x^2))/(3*x) - 256*(-1 + x)*H[0, x])* - H[0, 0, -1, -1, x] + ((-256*(5 + 157*x - 15*x^2 + 5*x^3))/(15*x) + - 256*(1 + 2*x)*H[0, x])*H[0, 0, -1, 1, x] + - ((32*(-8080 + 4782*x - 2121*x^2 + 80*x^3))/(45*x) - - 128*(-5 + 11*x)*H[0, x])*H[0, 0, 0, -1, x] + + H[0, 0, -1, -1, x] + ((-256*(5 + 157*x - 15*x^2 + 5*x^3))/(15*x) + + 256*(1 + 2*x)*H[0, x])*H[0, 0, -1, 1, x] + + ((32*(-8080 + 4782*x - 2121*x^2 + 80*x^3))/(45*x) - + 128*(-5 + 11*x)*H[0, x])*H[0, 0, 0, -1, x] + ((-32*(-2660 - 786*x + 255*x^2 + 320*x^3))/(45*x) + 256*(2 + 3*x)*H[0, x])* - H[0, 0, 0, 1, x] + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + - 256*(1 + 2*x)*H[0, x])*H[0, 0, 1, -1, x] + + H[0, 0, 0, 1, x] + ((-256*(1 + x)*(1 - 4*x + x^2))/(3*x) + + 256*(1 + 2*x)*H[0, x])*H[0, 0, 1, -1, x] + ((32*(1160 + 353*x - 37*x^2 + 40*x^3))/(15*x) - (256*(1 + x)*H[0, x])/3)* - H[0, 0, 1, 1, x] + ((16*(-8 + 165*x - 159*x^2 + 4*x^3))/(9*x) + - 64*(1 + x)*H[0, x])*H[0, 1, 1, 1, x] + + H[0, 0, 1, 1, x] + ((16*(-8 + 165*x - 159*x^2 + 4*x^3))/(9*x) + + 64*(1 + x)*H[0, x])*H[0, 1, 1, 1, x] + 512*(-1 + x)*H[0, -1, 0, -1, -1, x] + 1024*(-1 + x)* - H[0, 0, -1, -1, -1, x] + 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - - 768*x*H[0, 0, -1, 0, 1, x] + 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - - 2304*x*H[0, 0, 0, -1, 1, x] + (2048*(-1 + 4*x)*H[0, 0, 0, 0, -1, x])/3 - - (128*(19 + 31*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*x*H[0, 0, 0, 1, -1, x] + - (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*x*H[0, 0, 1, 0, -1, x] + - 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - - 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + - CA*(TF^2*((16*(245035 - 45308*x + 197365*x^2 - 167815*x^3 - 120420*x^4 + + H[0, 0, -1, -1, -1, x] + 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - + 768*x*H[0, 0, -1, 0, 1, x] + 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - + 2304*x*H[0, 0, 0, -1, 1, x] + (2048*(-1 + 4*x)*H[0, 0, 0, 0, -1, x])/3 - + (128*(19 + 31*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*x*H[0, 0, 0, 1, -1, x] + + (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*x*H[0, 0, 1, 0, -1, x] + + 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + + CA*(TF^2*((16*(245035 - 45308*x + 197365*x^2 - 167815*x^3 - 120420*x^4 + 24192*x^5))/(25515*x) - (16*(-350 + 1353*x + 114*x^2 + 350*x^3)*z3)/ - (135*x) + (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - - 19744*x^5 + 21504*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1)}, x])/(945*(-((-1 + x)*x))^(3/2)) + - (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - 19744*x^5 + + (135*x) + (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - + 19744*x^5 + 21504*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(945*(-((-1 + x)*x))^(3/2)) + + (8*(-1403 - 27089*x + 25450*x^2 + 52124*x^3 - 49792*x^4 - 19744*x^5 + 21504*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ (945*(-((-1 + x)*x))^(3/2)) - (512*(-6 + 83*x + 32*x^2)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1)}, x])/(45*x) - - (512*(-6 + 83*x + 32*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) + - (8*(-774 - 248268*x + 274039*x^2 - 11407*x^3 + 48672*x^4 - 117576*x^5 + - 48384*x^6)*H[0, x])/(8505*(-1 + x)) + - (4*(-11228 - 2121*x + 6939*x^2 + 4898*x^3)*H[0, x]^2)/(2835*(-1 + x)) + - (112*(1 + x)*H[0, x]^3)/81 + - ((8*(-28490 - 28416*x + 162417*x^2 - 31927*x^3 - 20520*x^4 - 69192*x^5 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(45*x) - + (512*(-6 + 83*x + 32*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(45*x) + + (8*(-774 - 248268*x + 274039*x^2 - 11407*x^3 + 48672*x^4 - 117576*x^5 + + 48384*x^6)*H[0, x])/(8505*(-1 + x)) + + (4*(-11228 - 2121*x + 6939*x^2 + 4898*x^3)*H[0, x]^2)/(2835*(-1 + x)) + + (112*(1 + x)*H[0, x]^3)/81 + + ((8*(-28490 - 28416*x + 162417*x^2 - 31927*x^3 - 20520*x^4 - 69192*x^5 + 48384*x^6))/(8505*x) - (8*(-655 + 789*x - 660*x^2 + 466*x^3)* - H[0, x])/(405*x) - (8*(1 - x + 4*x^2)*H[0, x]^2)/(15*x))*H[1, x] - - (4*(-395 + 624*x - 225*x^2 + 206*x^3)*H[1, x]^2)/(405*x) + + H[0, x])/(405*x) - (8*(1 - x + 4*x^2)*H[0, x]^2)/(15*x))*H[1, x] - + (4*(-395 + 624*x - 225*x^2 + 206*x^3)*H[1, x]^2)/(405*x) + z2*((-8*(16905 - 43918*x + 39984*x^2 - 38106*x^3 + 23623*x^4))/ - (2835*(-1 + x)*x) + (464*(1 + x)*H[0, x])/27 + - (16*(1 - x + 4*x^2)*H[1, x])/(15*x)) + + (2835*(-1 + x)*x) + (464*(1 + x)*H[0, x])/27 + + (16*(1 - x + 4*x^2)*H[1, x])/(15*x)) + ((8*(4585 - 15806*x + 14847*x^2 - 15118*x^3 + 9980*x^4))/ - (2835*(-1 + x)*x) + (8*(18 + 133*x + 160*x^2)*H[0, x])/(135*x) - - (16*(1 - x + 4*x^2)*H[1, x])/(15*x))*H[0, 1, x] - - (16*(9 + 182*x + 164*x^2)*H[0, 0, 1, x])/(135*x) + - (8*(36 + 35*x + 152*x^2)*H[0, 1, 1, x])/(135*x) + - NF*((-8*(-13532 + 16627*x - 16271*x^2 + 20120*x^3))/(729*x) + - (64*(-7 + 18*x - 3*x^2 + 7*x^3)*z3)/(27*x) - - (8*(582 + 2127*x - 3607*x^2 + 1078*x^3)*H[0, x])/(243*(-1 + x)) - + (2835*(-1 + x)*x) + (8*(18 + 133*x + 160*x^2)*H[0, x])/(135*x) - + (16*(1 - x + 4*x^2)*H[1, x])/(15*x))*H[0, 1, x] - + (16*(9 + 182*x + 164*x^2)*H[0, 0, 1, x])/(135*x) + + (8*(36 + 35*x + 152*x^2)*H[0, 1, 1, x])/(135*x) + + NF*((-8*(-13532 + 16627*x - 16271*x^2 + 20120*x^3))/(729*x) + + (64*(-7 + 18*x - 3*x^2 + 7*x^3)*z3)/(27*x) - + (8*(582 + 2127*x - 3607*x^2 + 1078*x^3)*H[0, x])/(243*(-1 + x)) - (4*(-236 - 467*x + 52*x^2)*H[0, x]^2)/81 + (224*(1 + x)*H[0, x]^3)/ - 81 + z2*((-8*(-138 + 406*x + 175*x^2 + 190*x^3))/(81*x) - - (32*(1 + x)*H[0, x])/27) + - ((-8*(-358 + 111*x - 1263*x^2 + 1078*x^3))/(243*x) - - (8*(-52 + 33*x - 21*x^2 + 52*x^3)*H[0, x])/(81*x))*H[1, x] + - (4*(-52 + 33*x - 81*x^2 + 52*x^3)*H[1, x]^2)/(81*x) + + 81 + z2*((-8*(-138 + 406*x + 175*x^2 + 190*x^3))/(81*x) - + (32*(1 + x)*H[0, x])/27) + + ((-8*(-358 + 111*x - 1263*x^2 + 1078*x^3))/(243*x) - + (8*(-52 + 33*x - 21*x^2 + 52*x^3)*H[0, x])/(81*x))*H[1, x] + + (4*(-52 + 33*x - 81*x^2 + 52*x^3)*H[1, x]^2)/(81*x) + ((8*(-52 + 265*x + 268*x^2 + 104*x^3))/(81*x) + (128*(1 + x)*H[0, x])/ - 27)*H[0, 1, x] - (128*(1 + x)*H[0, 0, 1, x])/27 - - (128*(1 + x)*H[0, 1, 1, x])/27)) + - CF*TF*((-32*B4*(-260 + 87*x + 44*x^2 + 10*x^3))/(15*x) - - (4*(272160 - 9336320*x - 3300025*x^2 + 7190304*x^3 + 50470205*x^4 - + 27)*H[0, 1, x] - (128*(1 + x)*H[0, 0, 1, x])/27 - + (128*(1 + x)*H[0, 1, 1, x])/27)) + + CF*TF*((-32*B4*(-260 + 87*x + 44*x^2 + 10*x^3))/(15*x) - + (4*(272160 - 9336320*x - 3300025*x^2 + 7190304*x^3 + 50470205*x^4 - 62944172*x^5 + 24337368*x^6 - 6242400*x^7 + 103680*x^8))/ - (18225*(-1 + x)*x^2) + (16*(111 + 883*x)*z5)/3 + + (18225*(-1 + x)*x^2) + (16*(111 + 883*x)*z5)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - + ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - 258486*x^5 + 68760*x^6 - 960*x^7 - 1200*Sqrt[1 - x]*x^(3/2)* Sqrt[-((-1 + x)*x)] + 2400*Sqrt[1 - x]*x^(5/2)* - Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1)}, x]) - - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1)}, x]) - + (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ - (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/ - (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (15*x) - (4096*(-125 - 13*x + 22*x^2)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/ - (15*x) - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], + (15*x) - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + 8192*(1 + x)* GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - 16384*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - 24576*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + - ((-8*(-45360 + 356290*x - 844475*x^2 - 5885706*x^3 + 2623012*x^4 + - 15691737*x^5 - 23404896*x^6 + 14995908*x^7 - 3510000*x^8 + - 51840*x^9))/(6075*(-1 + x)*x^2) + + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + ((-8*(-45360 + 356290*x - 844475*x^2 - 5885706*x^3 + 2623012*x^4 + + 15691737*x^5 - 23404896*x^6 + 14995908*x^7 - 3510000*x^8 + + 51840*x^9))/(6075*(-1 + x)*x^2) + (8*(1 + x)*(-16197 + 7915*x + 167*x^2 + 4579*x^3)*H[-1, x])/ (135*x^2) - (8*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4)* H[-1, x]^2)/(45*x^3) - (32*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x]^3)/ - (27*x))*H[0, x] + - ((-4*(15120 + 245160*x - 1050320*x^2 + 300450*x^3 + 483824*x^4 + - 3741*x^5))/(2025*(-1 + x)*x^2) + + (27*x))*H[0, x] + + ((-4*(15120 + 245160*x - 1050320*x^2 + 300450*x^3 + 483824*x^4 + + 3741*x^5))/(2025*(-1 + x)*x^2) + (4*(1 + x)*(-1512 - 13128*x + 23270*x^2 - 10781*x^3 + 4580*x^4)* H[-1, x])/(135*x^3) - (8*(1 + x)*(28 + 101*x + 28*x^2)*H[-1, x]^2)/ (9*x))*H[0, x]^2 + ((-4*(-288 + 2689*x - 4943*x^2 + 334*x^3))/ (81*x) + (8*(1 + x)*(-8 + 12*x - 25*x^2 + 16*x^3)*H[-1, x])/(9*x^2))* H[0, x]^3 + (4*(-74 + 91*x)*H[0, x]^4)/27 + (4*(-5 + 9*x)*H[0, x]^5)/ 15 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2* - ((1024*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 4096*(1 + x)*H[0, x]) + + ((1024*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 4096*(1 + x)*H[0, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2* - ((1024*(240 - 49*x + 21*x^2 + 10*x^3))/(15*x) - 4096*(1 + x)*H[0, x]) + - z4*((4*(-53780 + 9019*x + 10387*x^2 + 1000*x^3))/(45*x) + - (8*(19 + 550*x)*H[0, x])/3) + + ((1024*(240 - 49*x + 21*x^2 + 10*x^3))/(15*x) - 4096*(1 + x)*H[0, x]) + + z4*((4*(-53780 + 9019*x + 10387*x^2 + 1000*x^3))/(45*x) + + (8*(19 + 550*x)*H[0, x])/3) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - + ((64*(-4480 + 49664*x - 66471*x^2 - 122126*x^3 + 334099*x^4 - 258486*x^5 + 68760*x^6 - 960*x^7 - 1200*Sqrt[1 - x]*x^(3/2)* Sqrt[-((-1 + x)*x)] + 2400*Sqrt[1 - x]*x^(5/2)* - Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[-((-1 + x)*x)]))/(225*(-((-1 + x)*x))^(3/2)) + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - ((2048*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 8192*(1 + x)*H[0, x])) + - ((-8*(-15120 - 216235*x + 934785*x^2 - 2027062*x^3 + 906369*x^4 + + ((2048*(-2 - 15*x + 13*x^2 + 2*x^3))/(3*x) - 8192*(1 + x)*H[0, x])) + + ((-8*(-15120 - 216235*x + 934785*x^2 - 2027062*x^3 + 906369*x^4 + 4378379*x^5 - 7801632*x^6 + 4998636*x^7 - 1170000*x^8 + 17280*x^9))/ - (2025*(-1 + x)*x^2) + - ((-8*(8629 - 20936*x + 5657*x^2 - 11766*x^3 + 18596*x^4))/(135*x^2) - + (2025*(-1 + x)*x^2) + + ((-8*(8629 - 20936*x + 5657*x^2 - 11766*x^3 + 18596*x^4))/(135*x^2) - (64*(-1 + x)*(-42 + 348*x + 571*x^2 + 370*x^3 + 61*x^4)*H[-1, x])/ - (45*x^3))*H[0, x] + (4*(504 - 5160*x - 8330*x^2 + 11955*x^3 - - 1125*x^4 + 1886*x^5)*H[0, x]^2)/(135*x^3) + + (45*x^3))*H[0, x] + (4*(504 - 5160*x - 8330*x^2 + 11955*x^3 - + 1125*x^4 + 1886*x^5)*H[0, x]^2)/(135*x^3) + (8*(-1 + x)*(24 + 20*x + 137*x^2 + 32*x^3)*H[0, x]^3)/(27*x^2))* - H[1, x] + ((4*(-1 + x)*(-768 + 316*x - 590*x^2 + 1579*x^3))/(81*x^2) - - (16*(-4 - 30*x - 73*x^2 + 62*x^3 + 48*x^4)*H[0, x])/(9*x^2) - + H[1, x] + ((4*(-1 + x)*(-768 + 316*x - 590*x^2 + 1579*x^3))/(81*x^2) - + (16*(-4 - 30*x - 73*x^2 + 62*x^3 + 48*x^4)*H[0, x])/(9*x^2) - (4*(-1 + x)*(24 + 28*x + 181*x^2 + 40*x^3)*H[0, x]^2)/(9*x^2))* - H[1, x]^2 + ((4*(-1 + x)*(10 + 127*x + 172*x^2))/(81*x) - - (16*(-1 + x)*(10 + 13*x + 10*x^2)*H[0, x])/(27*x))*H[1, x]^3 + - (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) + - (128*(-390 + 201*x^2 + 61*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + - ((-8*(1 + x)*(-16197 + 7915*x + 167*x^2 + 4579*x^3))/(135*x^2) + + H[1, x]^2 + ((4*(-1 + x)*(10 + 127*x + 172*x^2))/(81*x) - + (16*(-1 + x)*(10 + 13*x + 10*x^2)*H[0, x])/(27*x))*H[1, x]^3 + + (2*(-1 + x)*(4 + 7*x + 4*x^2)*H[1, x]^4)/(27*x) + + (128*(-390 + 201*x^2 + 61*x^4)*H[0, x]*H[-1, 1, x])/(45*x^2) + + ((-8*(1 + x)*(-16197 + 7915*x + 167*x^2 + 4579*x^3))/(135*x^2) + (16*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4)*H[-1, x])/ - (45*x^3) + (32*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x]^2)/(9*x) + + (45*x^3) + (32*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x]^2)/(9*x) + ((-8*(-504 - 4560*x + 3714*x^2 + 1123*x^3 - 1647*x^4 + 2004*x^5))/ (45*x^3) + (32*(1 + x)*(12 + 52*x + 83*x^2 + 46*x^3)*H[-1, x])/ - (9*x^2))*H[0, x] - (8*(-120 - 4700*x + 756*x^2 - 3441*x^3 + - 160*x^4)*H[0, x]^2)/(45*x^2) + (176*(-1 + x)*H[0, x]^3)/9 + - ((64*(-1 + x)*(-42 + 348*x + 571*x^2 + 370*x^3 + 61*x^4))/(45*x^3) - + (9*x^2))*H[0, x] - (8*(-120 - 4700*x + 756*x^2 - 3441*x^3 + + 160*x^4)*H[0, x]^2)/(45*x^2) + (176*(-1 + x)*H[0, x]^3)/9 + + ((64*(-1 + x)*(-42 + 348*x + 571*x^2 + 370*x^3 + 61*x^4))/(45*x^3) - (64*(-1 + x)*(17 + 50*x + 17*x^2)*H[0, x])/(9*x))*H[1, x])* H[0, -1, x] + ((-16*(-12 - 396*x + 39*x^2 - 174*x^3 + 10*x^4))/ - (9*x^2) - (32*(-1 + x)*H[0, x])/3)*H[0, -1, x]^2 + - ((8*(144555 - 761190*x + 895205*x^2 - 207590*x^3 + 324424*x^4 - - 659503*x^5 + 269499*x^6))/(2025*(-1 + x)^2*x^2) - + (9*x^2) - (32*(-1 + x)*H[0, x])/3)*H[0, -1, x]^2 + + ((8*(144555 - 761190*x + 895205*x^2 - 207590*x^3 + 324424*x^4 - + 659503*x^5 + 269499*x^6))/(2025*(-1 + x)^2*x^2) - (64*(1 + x)*(-42 - 343*x + 576*x^2 - 205*x^3 + 26*x^4)*H[-1, x])/ - (45*x^3) - (448*(1 + x)^3*H[-1, x]^2)/(9*x) + - ((-8*(-504 + 6144*x + 4010*x^2 - 26835*x^3 + 39390*x^4 - 22715*x^5 + - 870*x^6))/(135*(-1 + x)*x^3) - + (45*x^3) - (448*(1 + x)^3*H[-1, x]^2)/(9*x) + + ((-8*(-504 + 6144*x + 4010*x^2 - 26835*x^3 + 39390*x^4 - 22715*x^5 + + 870*x^6))/(135*(-1 + x)*x^3) - (32*(1 + x)*(12 + 28*x + 29*x^2 + 22*x^3)*H[-1, x])/(9*x^2))* H[0, x] - (8*(-24 + 380*x + 41*x^2 + 365*x^3 + 96*x^4)*H[0, x]^2)/ - (9*x^2) - (208*(1 + x)*H[0, x]^3)/9 + - ((16*(504 - 4944*x + 4094*x^2 + 11713*x^3 - 18429*x^4 + 6364*x^5 + - 518*x^6))/(135*(-1 + x)*x^3) + + (9*x^2) - (208*(1 + x)*H[0, x]^3)/9 + + ((16*(504 - 4944*x + 4094*x^2 + 11713*x^3 - 18429*x^4 + 6364*x^5 + + 518*x^6))/(135*(-1 + x)*x^3) + (16*(-24 - 16*x - 297*x^2 + 273*x^3 + 52*x^4)*H[0, x])/(9*x^2))* - H[1, x] + (16*(-6 - 21*x + 19*x^2 + 6*x^3)*H[1, x]^2)/(3*x) + - ((-32*(1330 + 228*x + 1023*x^2 + 170*x^3))/(45*x) + - (832*(1 + x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + - ((-16*(-120 - 1150*x + 507*x^2 - 123*x^3 + 20*x^4))/(45*x^2) - - (560*(1 + x)*H[0, x])/3)*H[0, 1, x]^2 + + H[1, x] + (16*(-6 - 21*x + 19*x^2 + 6*x^3)*H[1, x]^2)/(3*x) + + ((-32*(1330 + 228*x + 1023*x^2 + 170*x^3))/(45*x) + + (832*(1 + x)*H[0, x])/3)*H[0, -1, x])*H[0, 1, x] + + ((-16*(-120 - 1150*x + 507*x^2 - 123*x^3 + 20*x^4))/(45*x^2) - + (560*(1 + x)*H[0, x])/3)*H[0, 1, x]^2 + z3*((4*(-156468 + 196381*x + 79647*x^2 - 127206*x^3 + 9806*x^4))/ (135*(-1 + x)*x) - (16*(1 + x)*(4 + 20*x + 53*x^2 + 18*x^3)*H[-1, x])/ - (3*x^2) + (16*(-340 - 805*x + 4397*x^2)*H[0, x])/(45*x) - - (16*(-5 + 34*x)*H[0, x]^2)/3 + (16*(16 - 34*x + 25*x^2 - 5*x^3 + - 10*x^4)*H[1, x])/(3*x^2) + (256*(-1 + x)*H[0, -1, x])/3 - - (128*(1 + x)*H[0, 1, x])/3) + - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + - 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - - (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + + (3*x^2) + (16*(-340 - 805*x + 4397*x^2)*H[0, x])/(45*x) - + (16*(-5 + 34*x)*H[0, x]^2)/3 + (16*(16 - 34*x + 25*x^2 - 5*x^3 + + 10*x^4)*H[1, x])/(3*x^2) + (256*(-1 + x)*H[0, -1, x])/3 - + (128*(1 + x)*H[0, 1, x])/3) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + + 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - + (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + 4096*(1 + x)*H[0, x]^2 - (2048*(-2 - 15*x + 13*x^2 + 2*x^3)*H[1, x])/ - (3*x) + 8192*(1 + x)*H[0, 1, x]) + - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + - 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - - (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + + (3*x) + 8192*(1 + x)*H[0, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x]*((256*(-112 + 1152*x - 2214*x^2 - 1827*x^3 + + 5549*x^4 - 2500*x^5 + 32*x^6))/(15*(-1 + x)*x^3) - + (2048*(240 - 49*x + 21*x^2 + 10*x^3)*H[0, x])/(15*x) + 4096*(1 + x)*H[0, x]^2 - (2048*(-2 - 15*x + 13*x^2 + 2*x^3)*H[1, x])/ - (3*x) + 8192*(1 + x)*H[0, 1, x]) + - ((-16*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4))/(45*x^3) - - (64*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x])/(9*x) - - (32*(24 + 460*x + 96*x^2 + 303*x^3 + 36*x^4)*H[0, x])/(9*x^2) + + (3*x) + 8192*(1 + x)*H[0, 1, x]) + + ((-16*(1 + x)*(-168 - 1572*x + 3342*x^2 - 397*x^3 + 312*x^4))/(45*x^3) - + (64*(1 + x)*(2 - 29*x + 2*x^2)*H[-1, x])/(9*x) - + (32*(24 + 460*x + 96*x^2 + 303*x^3 + 36*x^4)*H[0, x])/(9*x^2) + 64*(-1 + x)*H[0, x]^2 + (512*(-1 + x)*H[0, -1, x])/3)* - H[0, -1, -1, x] + ((-64*(42 - 395*x - 233*x^2 + 31*x^3 + 179*x^4 + - 96*x^5))/(45*x^3) + (896*(1 + x)^3*H[-1, x])/(9*x) + + H[0, -1, -1, x] + ((-64*(42 - 395*x - 233*x^2 + 31*x^3 + 179*x^4 + + 96*x^5))/(45*x^3) + (896*(1 + x)^3*H[-1, x])/(9*x) + (32*(60 + 1530*x - 603*x^2 + 1278*x^3 + 280*x^4)*H[0, x])/(45*x^2))* - H[0, -1, 1, x] + ((8*(-1512 - 12720*x + 12142*x^2 - 5751*x^3 - - 3681*x^4 + 7444*x^5))/(135*x^3) - - (32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3)*H[-1, x])/(9*x^2) - - (16*(120 + 9460*x - 1803*x^2 + 6747*x^3 + 520*x^4)*H[0, x])/(45*x^2) - + H[0, -1, 1, x] + ((8*(-1512 - 12720*x + 12142*x^2 - 5751*x^3 - + 3681*x^4 + 7444*x^5))/(135*x^3) - + (32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3)*H[-1, x])/(9*x^2) - + (16*(120 + 9460*x - 1803*x^2 + 6747*x^3 + 520*x^4)*H[0, x])/(45*x^2) - (64*(-10 + 19*x)*H[0, x]^2)/3 + (128*(-1 + x)*(17 + 50*x + 17*x^2)* - H[1, x])/(9*x) - (256*(-1 + x)*H[0, -1, x])/3 - - (1664*(1 + x)*H[0, 1, x])/3)*H[0, 0, -1, x] + - ((-8*(504 - 6624*x - 3410*x^2 + 41115*x^3 - 64470*x^4 + 30839*x^5 + - 1326*x^6))/(135*(-1 + x)*x^3) + - (64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3)*H[-1, x])/(3*x^2) + + H[1, x])/(9*x) - (256*(-1 + x)*H[0, -1, x])/3 - + (1664*(1 + x)*H[0, 1, x])/3)*H[0, 0, -1, x] + + ((-8*(504 - 6624*x - 3410*x^2 + 41115*x^3 - 64470*x^4 + 30839*x^5 + + 1326*x^6))/(135*(-1 + x)*x^3) + + (64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3)*H[-1, x])/(3*x^2) + (16*(-120 + 3780*x + 1006*x^2 + 4405*x^3 + 1040*x^4)*H[0, x])/ - (45*x^2) + (32*(28 + 23*x)*H[0, x]^2)/3 - - (16*(8 - 20*x - 91*x^2 + 87*x^3 + 8*x^4)*H[1, x])/(3*x^2) + - (1312*(1 + x)*H[0, 1, x])/3)*H[0, 0, 1, x] + - ((64*(1 + x)*(-42 - 343*x + 576*x^2 - 205*x^3 + 26*x^4))/(45*x^3) + - (896*(1 + x)^3*H[-1, x])/(9*x) + + (45*x^2) + (32*(28 + 23*x)*H[0, x]^2)/3 - + (16*(8 - 20*x - 91*x^2 + 87*x^3 + 8*x^4)*H[1, x])/(3*x^2) + + (1312*(1 + x)*H[0, 1, x])/3)*H[0, 0, 1, x] + + ((64*(1 + x)*(-42 - 343*x + 576*x^2 - 205*x^3 + 26*x^4))/(45*x^3) + + (896*(1 + x)^3*H[-1, x])/(9*x) + (32*(60 + 1530*x + 513*x^2 + 1278*x^3 + 280*x^4)*H[0, x])/(45*x^2))* - H[0, 1, -1, x] + ((16*(-1008 + 10008*x - 7708*x^2 - 22171*x^3 + - 33393*x^4 - 12308*x^5 + 154*x^6))/(135*(-1 + x)*x^3) - - (256*(1 + x)^3*H[-1, x])/(9*x) - - (16*(-24 - 72*x - 563*x^2 + 301*x^3 + 60*x^4)*H[0, x])/(9*x^2) + - (272*(1 + x)*H[0, x]^2)/3 - (16*(24 - 88*x - 165*x^2 + 153*x^3 + - 52*x^4)*H[1, x])/(9*x^2) - 192*(1 + x)*H[0, 1, x])*H[0, 1, 1, x] + - z2*((8*(-15120 + 22650*x + 299575*x^2 - 677365*x^3 + 565421*x^4 - - 328352*x^5 + 127791*x^6))/(2025*(-1 + x)^2*x^2) + - (8*(17 + 19*x)*z3)/3 - (8*(1 + x)*(-336 - 3004*x + 5586*x^2 - - 3197*x^3 + 836*x^4)*H[-1, x])/(45*x^3) + - (16*(1 + x)*(26 + 85*x + 26*x^2)*H[-1, x]^2)/(9*x) + - ((-4*(1216 + 4949*x + 5675*x^2 + 422*x^3))/(27*x) - - (8*(1 + x)*(-1 + 4*x)*(8 + 8*x + 7*x^2)*H[-1, x])/(3*x^2))*H[0, x] + - (8*(-85 - 160*x + 12*x^2)*H[0, x]^2)/9 - (8*(41 + 23*x)*H[0, x]^3)/9 + + H[0, 1, -1, x] + ((16*(-1008 + 10008*x - 7708*x^2 - 22171*x^3 + + 33393*x^4 - 12308*x^5 + 154*x^6))/(135*(-1 + x)*x^3) - + (256*(1 + x)^3*H[-1, x])/(9*x) - + (16*(-24 - 72*x - 563*x^2 + 301*x^3 + 60*x^4)*H[0, x])/(9*x^2) + + (272*(1 + x)*H[0, x]^2)/3 - (16*(24 - 88*x - 165*x^2 + 153*x^3 + + 52*x^4)*H[1, x])/(9*x^2) - 192*(1 + x)*H[0, 1, x])*H[0, 1, 1, x] + + z2*((8*(-15120 + 22650*x + 299575*x^2 - 677365*x^3 + 565421*x^4 - + 328352*x^5 + 127791*x^6))/(2025*(-1 + x)^2*x^2) + + (8*(17 + 19*x)*z3)/3 - (8*(1 + x)*(-336 - 3004*x + 5586*x^2 - + 3197*x^3 + 836*x^4)*H[-1, x])/(45*x^3) + + (16*(1 + x)*(26 + 85*x + 26*x^2)*H[-1, x]^2)/(9*x) + + ((-4*(1216 + 4949*x + 5675*x^2 + 422*x^3))/(27*x) - + (8*(1 + x)*(-1 + 4*x)*(8 + 8*x + 7*x^2)*H[-1, x])/(3*x^2))*H[0, x] + + (8*(-85 - 160*x + 12*x^2)*H[0, x]^2)/9 - (8*(41 + 23*x)*H[0, x]^3)/9 + ((4*(-1560 - 8738*x - 2161*x^2 + 41058*x^3 - 30541*x^4 + 2662*x^5))/ (135*(-1 + x)*x^2) - (8*(-1 + x)*(120 + 64*x + 553*x^2 + 124*x^3)* H[0, x])/(9*x^2))*H[1, x] - (4*(-4 - 41*x + 33*x^2 + 4*x^3)* - H[1, x]^2)/(3*x) + ((8*(-120 - 6360*x + 2061*x^2 - 4611*x^3 + - 140*x^4))/(45*x^2) - (112*(-1 + x)*H[0, x])/3)*H[0, -1, x] + - ((8*(-600 + 1460*x + 4*x^2 + 3229*x^3 + 600*x^4))/(45*x^2) + + H[1, x]^2)/(3*x) + ((8*(-120 - 6360*x + 2061*x^2 - 4611*x^3 + + 140*x^4))/(45*x^2) - (112*(-1 + x)*H[0, x])/3)*H[0, -1, x] + + ((8*(-600 + 1460*x + 4*x^2 + 3229*x^3 + 600*x^4))/(45*x^2) + (688*(1 + x)*H[0, x])/3)*H[0, 1, x] - (256*(-1 + x)*H[0, -1, -1, x])/ - 3 + (32*(-19 + 55*x)*H[0, 0, -1, x])/3 - - (16*(91 + 115*x)*H[0, 0, 1, x])/3 + (208*(1 + x)*H[0, 1, 1, x])/3) + + 3 + (32*(-19 + 55*x)*H[0, 0, -1, x])/3 - + (16*(91 + 115*x)*H[0, 0, 1, x])/3 + (208*(1 + x)*H[0, 1, 1, x])/3) + ((64*(1 + x)*(2 - 29*x + 2*x^2))/(9*x) - (512*(-1 + x)*H[0, x])/3)* - H[0, -1, -1, -1, x] - (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + - ((32*(-20 - 160*x + 77*x^2 + 105*x^3 + 30*x^4))/(15*x^2) - - (832*(1 + x)*H[0, x])/3)*H[0, -1, 0, 1, x] - - (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + - (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + - ((32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3))/(9*x^2) + - (896*(-1 + x)*H[0, x])/3)*H[0, 0, -1, -1, x] + - ((-64*(20 + 85*x - 222*x^2 + 140*x^3 + 55*x^4))/(15*x^2) - - (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + - ((16*(40 + 4740*x - 982*x^2 + 3351*x^3 + 600*x^4))/(15*x^2) + - (32*(-43 + 195*x)*H[0, x])/3)*H[0, 0, 0, -1, x] + - ((-16*(-120 + 5660*x + 1468*x^2 + 7945*x^3 + 1900*x^4))/(45*x^2) - - (32*(133 + 79*x)*H[0, x])/3)*H[0, 0, 0, 1, x] + - ((-64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3))/(3*x^2) - - (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + - ((16*(-120 - 5620*x - 1072*x^2 + 893*x^3 + 200*x^4))/(45*x^2) + - (1280*(1 + x)*H[0, x])/3)*H[0, 0, 1, 1, x] - - (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + - (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + - (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + - ((16*(72 - 172*x - 125*x^2 + 97*x^3 + 64*x^4))/(9*x^2) + - (64*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] - - (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 - - (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - - (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + - (256*(5 + 8*x)*H[0, 0, -1, 0, 1, x])/3 - + H[0, -1, -1, -1, x] - (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + + ((32*(-20 - 160*x + 77*x^2 + 105*x^3 + 30*x^4))/(15*x^2) - + (832*(1 + x)*H[0, x])/3)*H[0, -1, 0, 1, x] - + (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + + ((32*(1 + x)*(24 + 76*x + 65*x^2 + 64*x^3))/(9*x^2) + + (896*(-1 + x)*H[0, x])/3)*H[0, 0, -1, -1, x] + + ((-64*(20 + 85*x - 222*x^2 + 140*x^3 + 55*x^4))/(15*x^2) - + (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, -1, 1, x] + + ((16*(40 + 4740*x - 982*x^2 + 3351*x^3 + 600*x^4))/(15*x^2) + + (32*(-43 + 195*x)*H[0, x])/3)*H[0, 0, 0, -1, x] + + ((-16*(-120 + 5660*x + 1468*x^2 + 7945*x^3 + 1900*x^4))/(45*x^2) - + (32*(133 + 79*x)*H[0, x])/3)*H[0, 0, 0, 1, x] + + ((-64*(1 + x)*(4 + 13*x + 17*x^2 + 11*x^3))/(3*x^2) - + (128*(13 + 19*x)*H[0, x])/3)*H[0, 0, 1, -1, x] + + ((16*(-120 - 5620*x - 1072*x^2 + 893*x^3 + 200*x^4))/(45*x^2) + + (1280*(1 + x)*H[0, x])/3)*H[0, 0, 1, 1, x] - + (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + + ((16*(72 - 172*x - 125*x^2 + 97*x^3 + 64*x^4))/(9*x^2) + + (64*(1 + x)*H[0, x])/3)*H[0, 1, 1, 1, x] - + (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 - + (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - + (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + + (256*(5 + 8*x)*H[0, 0, -1, 0, 1, x])/3 - 640*(-1 + x)*H[0, 0, 0, -1, -1, x] + 128*(13 + 19*x)* - H[0, 0, 0, -1, 1, x] - (256*(3 + 46*x)*H[0, 0, 0, 0, -1, x])/3 + + H[0, 0, 0, -1, 1, x] - (256*(3 + 46*x)*H[0, 0, 0, 0, -1, x])/3 + 128*(22 + 9*x)*H[0, 0, 0, 0, 1, x] + 128*(13 + 19*x)* - H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + - (128*(13 + 19*x)*H[0, 0, 1, 0, -1, x])/3 - + H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + + (128*(13 + 19*x)*H[0, 0, 1, 0, -1, x])/3 - (2464*(1 + x)*H[0, 0, 1, 0, 1, x])/3 + 1120*(1 + x)* - H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - + H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3)); - REGPOL = CF*TF^2*((256*(-43 - 263*x + 441*x^2 - 630*x^3 + 180*x^4))/1215 + - (656*(1 + x)*z4)/9 + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + + REGPOL = CF*TF^2*((256*(-43 - 263*x + 441*x^2 - 630*x^3 + 180*x^4))/1215 + + (656*(1 + x)*z4)/9 + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + 960*x^4)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ - (135*x^(3/2)) + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + + (135*x^(3/2)) + (64*Sqrt[1 - x]*(7 + 516*x + 512*x^2 - 2400*x^3 + 960*x^4)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ - (135*x^(3/2)) - (8192*(-2 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/9 - + (135*x^(3/2)) - (8192*(-2 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/9 - (8192*(-2 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1)}, x])/9 + (8*(121 + 19*x)*H[0, x]^3)/81 + - (28*(1 + x)*H[0, x]^4)/27 + z3*((-16*(-175 + 11*x))/27 - - (224*(1 + x)*H[0, x])/9) - (416*(-1 + x)*H[1, x]^2)/27 - - (80*(-1 + x)*H[1, x]^3)/27 + (704*(-95 + 13*x)*H[0, 1, x])/405 - - (64*(1 + x)*H[0, 1, x]^2)/3 + - H[1, x]*((128*(-1 + x)*(137 + 375*x + 474*x^2 - 1080*x^3 + 360*x^4))/405 + - (320*(-1 + x)*H[0, 1, x])/3) + H[0, x]^2*((8*(1675 + 97*x))/405 + - (160*(-1 + x)*H[1, x])/9 - (64*(1 + x)*H[0, 1, x])/9) + - z2*((-8*(-9605 + 2389*x))/405 - (8*(-347 + 307*x)*H[0, x])/27 + - (232*(1 + x)*H[0, x]^2)/9 - (880*(-1 + x)*H[1, x])/9 + - (352*(1 + x)*H[0, 1, x])/9) + (128*(-37 + 35*x)*H[0, 0, 1, x])/27 - - (64*(-88 + 83*x)*H[0, 1, 1, x])/27 + - H[0, x]*((32*(8341 - 6071*x - 1188*x^2 + 18648*x^3 - 17280*x^4 + - 4320*x^5))/1215 - (1664*(-1 + x)*H[1, x])/27 - - (160*(-1 + x)*H[1, x]^2)/9 - (64*(-41 + 31*x)*H[0, 1, x])/27 + - (512*(1 + x)*H[0, 0, 1, x])/9 + (128*(1 + x)*H[0, 1, 1, x])/9) - - (1280*(1 + x)*H[0, 0, 0, 1, x])/9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + - (64*(1 + x)*H[0, 1, 1, 1, x])/9 + - NF*((-199040*(-1 + x))/243 + (208*(1 + x)*z4)/9 - - (16*(-97 + 41*x)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + - z3*((64*(-85 + 74*x))/27 - (640*(1 + x)*H[0, x])/9) + - (14848*(-1 + x)*H[1, x])/81 + (32*(-1 + x)*H[1, x]^2)/27 + - (560*(-1 + x)*H[1, x]^3)/27 - (256*(25 + 16*x)*H[0, 1, x])/81 + - z2*((16*(343 + 313*x))/81 - (16*(19 + 7*x)*H[0, x])/27 - - (16*(1 + x)*H[0, x]^2)/9 - (80*(-1 + x)*H[1, x])/9 + - (32*(1 + x)*H[0, 1, x])/9) + H[0, x]^2*((-16*(-419 + 19*x))/81 - - (160*(-1 + x)*H[1, x])/9 + (64*(1 + x)*H[0, 1, x])/9) - - (128*(2 + 11*x)*H[0, 0, 1, x])/27 + (64*(14 + 23*x)*H[0, 1, 1, x])/27 + - H[0, x]*((64*(1895 + 1133*x))/243 - (1216*(-1 + x)*H[1, x])/27 + - (160*(-1 + x)*H[1, x]^2)/9 + (128*(2 + 11*x)*H[0, 1, x])/27 - - (128*(1 + x)*H[0, 0, 1, x])/9 - (128*(1 + x)*H[0, 1, 1, x])/9) + - (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - - (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + - CA^2*TF*((32*B4*(1 + 9*x))/3 - - (2*(-9720 - 613369*x + 525603*x^2 + 216232*x^3 + 219780*x^4 - 558360*x^5 + - 209952*x^6))/(729*(-1 + x)*x) - (1184*(3 + x)*z5)/3 - + Sqrt[VarGL], VarGL^(-1)}, x])/9 + (8*(121 + 19*x)*H[0, x]^3)/81 + + (28*(1 + x)*H[0, x]^4)/27 + z3*((-16*(-175 + 11*x))/27 - + (224*(1 + x)*H[0, x])/9) - (416*(-1 + x)*H[1, x]^2)/27 - + (80*(-1 + x)*H[1, x]^3)/27 + (704*(-95 + 13*x)*H[0, 1, x])/405 - + (64*(1 + x)*H[0, 1, x]^2)/3 + + H[1, x]*((128*(-1 + x)*(137 + 375*x + 474*x^2 - 1080*x^3 + 360*x^4))/405 + + (320*(-1 + x)*H[0, 1, x])/3) + H[0, x]^2*((8*(1675 + 97*x))/405 + + (160*(-1 + x)*H[1, x])/9 - (64*(1 + x)*H[0, 1, x])/9) + + z2*((-8*(-9605 + 2389*x))/405 - (8*(-347 + 307*x)*H[0, x])/27 + + (232*(1 + x)*H[0, x]^2)/9 - (880*(-1 + x)*H[1, x])/9 + + (352*(1 + x)*H[0, 1, x])/9) + (128*(-37 + 35*x)*H[0, 0, 1, x])/27 - + (64*(-88 + 83*x)*H[0, 1, 1, x])/27 + + H[0, x]*((32*(8341 - 6071*x - 1188*x^2 + 18648*x^3 - 17280*x^4 + + 4320*x^5))/1215 - (1664*(-1 + x)*H[1, x])/27 - + (160*(-1 + x)*H[1, x]^2)/9 - (64*(-41 + 31*x)*H[0, 1, x])/27 + + (512*(1 + x)*H[0, 0, 1, x])/9 + (128*(1 + x)*H[0, 1, 1, x])/9) - + (1280*(1 + x)*H[0, 0, 0, 1, x])/9 + (640*(1 + x)*H[0, 0, 1, 1, x])/9 + + (64*(1 + x)*H[0, 1, 1, 1, x])/9 + + NF*((-199040*(-1 + x))/243 + (208*(1 + x)*z4)/9 - + (16*(-97 + 41*x)*H[0, x]^3)/81 + (56*(1 + x)*H[0, x]^4)/27 + + z3*((64*(-85 + 74*x))/27 - (640*(1 + x)*H[0, x])/9) + + (14848*(-1 + x)*H[1, x])/81 + (32*(-1 + x)*H[1, x]^2)/27 + + (560*(-1 + x)*H[1, x]^3)/27 - (256*(25 + 16*x)*H[0, 1, x])/81 + + z2*((16*(343 + 313*x))/81 - (16*(19 + 7*x)*H[0, x])/27 - + (16*(1 + x)*H[0, x]^2)/9 - (80*(-1 + x)*H[1, x])/9 + + (32*(1 + x)*H[0, 1, x])/9) + H[0, x]^2*((-16*(-419 + 19*x))/81 - + (160*(-1 + x)*H[1, x])/9 + (64*(1 + x)*H[0, 1, x])/9) - + (128*(2 + 11*x)*H[0, 0, 1, x])/27 + (64*(14 + 23*x)*H[0, 1, 1, x])/27 + + H[0, x]*((64*(1895 + 1133*x))/243 - (1216*(-1 + x)*H[1, x])/27 + + (160*(-1 + x)*H[1, x]^2)/9 + (128*(2 + 11*x)*H[0, 1, x])/27 - + (128*(1 + x)*H[0, 0, 1, x])/9 - (128*(1 + x)*H[0, 1, 1, x])/9) + + (128*(1 + x)*H[0, 0, 0, 1, x])/9 + (128*(1 + x)*H[0, 0, 1, 1, x])/9 - + (448*(1 + x)*H[0, 1, 1, 1, x])/9)) + + CA^2*TF*((32*B4*(1 + 9*x))/3 - + (2*(-9720 - 613369*x + 525603*x^2 + 216232*x^3 + 219780*x^4 - 558360*x^5 + + 209952*x^6))/(729*(-1 + x)*x) - (1184*(3 + x)*z5)/3 - (256*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^ - 2)/3 - (256*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, + 2)/3 - (256*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* ((32*(160 + 283*x + 1105*x^2 - 3702*x^3 + 2112*x^4))/ (9*Sqrt[-((-1 + x)*x)]) - (512*(-33 + 29*x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* ((32*(160 + 283*x + 1105*x^2 - 3702*x^3 + 2112*x^4))/ (9*Sqrt[-((-1 + x)*x)]) - 3072*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x]) + (128*(20 - 26*x + 43*x^2 - 429*x^3 + 376*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) + (128*(20 - 26*x + 43*x^2 - 429*x^3 + 376*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1)}, x])/(3*(-1 + x)*x^2) + - (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x])/(3*(-1 + x)*x^2) + + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + (2048*(2 + 3*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + - 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - - 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 6144*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 9216*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + (16*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[-1, x]^3*H[0, x])/ (27*x*(1 + x)) + (2*(-17 + 20*x + 5*x^2 - 24*x^3 + 12*x^4)*H[0, x]^4)/ - (27*(-1 + x)*(1 + x)) - (4*H[0, x]^5)/15 + + (27*(-1 + x)*(1 + x)) - (4*H[0, x]^5)/15 + z4*((2*(638 + 4250*x - 661*x^2 - 4145*x^3 + 12*x^4))/ (9*(-1 + x)*(1 + x)) + 32*(1 + x)*H[-1, x] - (4*(113 + 69*x)*H[0, x])/ - 3 - 28*(-1 + x)*H[1, x]) - + 3 - 28*(-1 + x)*H[1, x]) - (8*(-38 + 14*x + 147*x^2 - 46*x^3 - 141*x^4 + 4*x^5)*H[0, -1, x]^2)/ - (9*(-1 + x)*x*(1 + x)) + (8*(52 - 290*x - 65*x^2 + 290*x^3 + 55*x^4 + - 10*x^5)*H[0, 1, x]^2)/(9*(-1 + x)*x*(1 + x)) + - H[0, x]^3*((-4*(-520 + 559*x + 8*x^2))/81 - - (4*(44 + 149*x - 402*x^2 + 221*x^3 + 8*x^4)*H[1, x])/(27*(-1 + x)*x) + - (16*(-1 + x)*H[0, -1, x])/3 + (40*(1 + x)*H[0, 1, x])/3) + + (9*(-1 + x)*x*(1 + x)) + (8*(52 - 290*x - 65*x^2 + 290*x^3 + 55*x^4 + + 10*x^5)*H[0, 1, x]^2)/(9*(-1 + x)*x*(1 + x)) + + H[0, x]^3*((-4*(-520 + 559*x + 8*x^2))/81 - + (4*(44 + 149*x - 402*x^2 + 221*x^3 + 8*x^4)*H[1, x])/(27*(-1 + x)*x) + + (16*(-1 + x)*H[0, -1, x])/3 + (40*(1 + x)*H[0, 1, x])/3) + z3*((-2*(28707 + 16050*x - 28071*x^2 - 14990*x^3 + 496*x^4))/ - (27*(-1 + x)*(1 + x)) + 112*H[0, x]^2 + - H[-1, x]*((8*(50 + 37*x - 33*x^2 + 36*x^4))/(9*x*(1 + x)) - + (27*(-1 + x)*(1 + x)) + 112*H[0, x]^2 + + H[-1, x]*((8*(50 + 37*x - 33*x^2 + 36*x^4))/(9*x*(1 + x)) - 32*(1 + x)*H[0, x]) - (8*(-68 - 21*x + 150*x^2 - 89*x^3 + 8*x^4)* - H[1, x])/(9*(-1 + x)*x) + + H[1, x])/(9*(-1 + x)*x) + H[0, x]*((-8*(238 + 231*x - 319*x^2 - 284*x^3 + 84*x^4))/ - (9*(-1 + x)*(1 + x)) + 48*(-1 + x)*H[1, x]) + - (16*(-5 + 17*x)*H[0, -1, x])/3 - (32*(-1 + 8*x)*H[0, 1, x])/3) + + (9*(-1 + x)*(1 + x)) + 48*(-1 + x)*H[1, x]) + + (16*(-5 + 17*x)*H[0, -1, x])/3 - (32*(-1 + 8*x)*H[0, 1, x])/3) + H[-1, x]^2*((4*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)*H[0, x])/ (27*x^2) + (4*(22 - 18*x - 75*x^2 - 15*x^3 + 28*x^4)*H[0, x]^2)/ (9*x*(1 + x)) - (16*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[0, -1, x])/ - (9*x*(1 + x)) + (16*(1 + x)*(14 + 43*x + 14*x^2)*H[0, 1, x])/(9*x)) + - H[1, x]^2*((-954 + 1645*x - 371*x^2 - 54*x^3)/(27*x) - - (4*(12 + 92*x - 237*x^2 + 119*x^3 + 6*x^4)*H[0, 1, x])/(9*(-1 + x)*x)) + - (8*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)*H[0, -1, -1, x])/(27*x^2) + - (8*(90 - 53*x - 48*x^2 - 525*x^3 + 136*x^4)*H[0, -1, 1, x])/(27*x^2) + + (9*x*(1 + x)) + (16*(1 + x)*(14 + 43*x + 14*x^2)*H[0, 1, x])/(9*x)) + + H[1, x]^2*((-954 + 1645*x - 371*x^2 - 54*x^3)/(27*x) - + (4*(12 + 92*x - 237*x^2 + 119*x^3 + 6*x^4)*H[0, 1, x])/(9*(-1 + x)*x)) + + (8*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)*H[0, -1, -1, x])/(27*x^2) + + (8*(90 - 53*x - 48*x^2 - 525*x^3 + 136*x^4)*H[0, -1, 1, x])/(27*x^2) + (4*(-270 + 299*x + 1706*x^2 - 5120*x^3 - 1100*x^4 + 5357*x^5 + 56*x^6)* - H[0, 0, -1, x])/(27*(-1 + x)*x^2*(1 + x)) + + H[0, 0, -1, x])/(27*(-1 + x)*x^2*(1 + x)) + (4*(90 - 747*x - 807*x^2 + 3030*x^3 - 327*x^4 - 2839*x^5 + 632*x^6)* - H[0, 0, 1, x])/(27*(-1 + x)*x^2*(1 + x)) + - (8*(1 + x)*(90 + 127*x - 175*x^2 + 136*x^3)*H[0, 1, -1, x])/(27*x^2) + + H[0, 0, 1, x])/(27*(-1 + x)*x^2*(1 + x)) + + (8*(1 + x)*(90 + 127*x - 175*x^2 + 136*x^3)*H[0, 1, -1, x])/(27*x^2) + H[0, -1, x]*((-16*(927 + 5978*x + 8862*x^2 + 4340*x^3 + 81*x^4))/ (81*x*(1 + x)) + (32*(85 - 168*x + 83*x^2 + 4*x^3)*H[0, 1, x])/ - (9*(-1 + x)) + (256*(-1 + x)*H[0, -1, -1, x])/3 - - 64*(-1 + x)*H[0, -1, 1, x] + (224*(-1 + x)*H[0, 0, -1, x])/3 - - (32*(-17 + 5*x)*H[0, 0, 1, x])/3 - 64*(-1 + x)*H[0, 1, -1, x]) - + (9*(-1 + x)) + (256*(-1 + x)*H[0, -1, -1, x])/3 - + 64*(-1 + x)*H[0, -1, 1, x] + (224*(-1 + x)*H[0, 0, -1, x])/3 - + (32*(-17 + 5*x)*H[0, 0, 1, x])/3 - 64*(-1 + x)*H[0, 1, -1, x]) - (8*(-180 + 72*x - 2401*x^2 + 5355*x^3 - 3044*x^4 + 108*x^5)*H[0, 1, 1, x])/ (27*(-1 + x)*x^2) + H[0, x]^2* - ((-1080 + 9828*x - 21167*x^2 + 2231*x^3 + 25777*x^4 - 16183*x^5 - + ((-1080 + 9828*x - 21167*x^2 + 2231*x^3 + 25777*x^4 - 16183*x^5 - 486*x^6)/(81*(-1 + x)^2*x*(1 + x)) - 1536*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - 1536*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + (2*(52 + 5*x - 93*x^2 + 58*x^3 + 30*x^4)*H[1, x]^2)/ - (9*(-1 + x)*x) - (4*(-52 + 237*x + 267*x^2 - 341*x^3 - 283*x^4 + - 56*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + (9*(-1 + x)*x) - (4*(-52 + 237*x + 267*x^2 - 341*x^3 - 283*x^4 + + 56*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + (4*(44 + 41*x - 481*x^2 - 65*x^3 + 431*x^4 + 38*x^5)*H[0, 1, x])/ (9*(-1 + x)*x*(1 + x)) + H[1, x]* ((-2*(-90 + 405*x + 850*x^2 - 2229*x^3 + 1144*x^4 + 72*x^5))/ - (27*(-1 + x)*x^2) + 48*(-1 + x)*H[0, -1, x] - - 16*(-1 + x)*H[0, 1, x]) + 48*(-1 + x)*H[0, -1, -1, x] - - 32*(-1 + 2*x)*H[0, -1, 1, x] - (80*(-5 + 2*x)*H[0, 0, -1, x])/3 - - (16*(21 + 23*x)*H[0, 0, 1, x])/3 - 32*(-1 + 2*x)*H[0, 1, -1, x] + - (64*(-2 + x)*H[0, 1, 1, x])/3) + - z2*((2*(1080 + 7656*x + 21800*x^2 - 37561*x^3 - 28192*x^4 + 32571*x^5 + - 810*x^6))/(81*(-1 + x)^2*x*(1 + x)) - (16*(1 + 4*x)*z3)/3 - - (8*(24 + 73*x + 105*x^2 + 74*x^3 + 26*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + + (27*(-1 + x)*x^2) + 48*(-1 + x)*H[0, -1, x] - + 16*(-1 + x)*H[0, 1, x]) + 48*(-1 + x)*H[0, -1, -1, x] - + 32*(-1 + 2*x)*H[0, -1, 1, x] - (80*(-5 + 2*x)*H[0, 0, -1, x])/3 - + (16*(21 + 23*x)*H[0, 0, 1, x])/3 - 32*(-1 + 2*x)*H[0, 1, -1, x] + + (64*(-2 + x)*H[0, 1, 1, x])/3) + + z2*((2*(1080 + 7656*x + 21800*x^2 - 37561*x^3 - 28192*x^4 + 32571*x^5 + + 810*x^6))/(81*(-1 + x)^2*x*(1 + x)) - (16*(1 + 4*x)*z3)/3 - + (8*(24 + 73*x + 105*x^2 + 74*x^3 + 26*x^4)*H[-1, x]^2)/(9*x*(1 + x)) + 8*(1 + x)*H[0, x]^3 + (4*(8 + 35*x - 114*x^2 + 63*x^3)*H[1, x]^2)/ (9*(-1 + x)*x) + H[0, x]^2* - ((-4*(61 - 174*x - 89*x^2 + 174*x^3 + 26*x^4))/(9*(-1 + x)*(1 + x)) - - 8*(-1 + x)*H[1, x]) + (8*(-26 + 270*x + 131*x^2 - 310*x^3 - 165*x^4 + - 40*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + ((-4*(61 - 174*x - 89*x^2 + 174*x^3 + 26*x^4))/(9*(-1 + x)*(1 + x)) - + 8*(-1 + x)*H[1, x]) + (8*(-26 + 270*x + 131*x^2 - 310*x^3 - 165*x^4 + + 40*x^5)*H[0, -1, x])/(9*(-1 + x)*x*(1 + x)) + H[1, x]*((8*(175 + 647*x - 1839*x^2 + 1058*x^3 + 4*x^4))/ - (27*(-1 + x)*x) - 32*(-1 + x)*H[0, -1, x]) - + (27*(-1 + x)*x) - 32*(-1 + x)*H[0, -1, x]) - (8*(142 - 104*x - 491*x^2 + 76*x^3 + 415*x^4 + 50*x^5)*H[0, 1, x])/ (9*(-1 + x)*x*(1 + x)) + H[-1, x]* - ((-16*(15 + 11*x + 71*x^2 + 71*x^3 + 2*x^4))/(9*x^2) + - (8*(22 + 237*x + 435*x^2 + 268*x^3 + 36*x^4)*H[0, x])/(9*x*(1 + x)) + - 8*(1 + x)*H[0, x]^2 + 32*(1 + x)*H[0, 1, x]) + + ((-16*(15 + 11*x + 71*x^2 + 71*x^3 + 2*x^4))/(9*x^2) + + (8*(22 + 237*x + 435*x^2 + 268*x^3 + 36*x^4)*H[0, x])/(9*x*(1 + x)) + + 8*(1 + x)*H[0, x]^2 + 32*(1 + x)*H[0, 1, x]) + H[0, x]*((-4*(1184 + 673*x - 1396*x^2 - 969*x^3 + 112*x^4))/ (27*(-1 + x)*(1 + x)) + (16*(63 - 31*x - 111*x^2 + 74*x^3 + 21*x^4)* - H[1, x])/(9*(-1 + x)*x) - (32*(-2 + 5*x)*H[0, -1, x])/3 - - (32*(8 + 5*x)*H[0, 1, x])/3) - (64*(-1 + x)*H[0, -1, -1, x])/3 - - 64*H[0, -1, 1, x] + (16*(-43 + 13*x)*H[0, 0, -1, x])/3 + - (32*(17 + 12*x)*H[0, 0, 1, x])/3 - 64*H[0, 1, -1, x] - - (80*(1 + x)*H[0, 1, 1, x])/3) + - H[0, 1, x]*((-2*(-1431 - 19960*x + 70276*x^2 - 75515*x^3 + 25388*x^4 + + H[1, x])/(9*(-1 + x)*x) - (32*(-2 + 5*x)*H[0, -1, x])/3 - + (32*(8 + 5*x)*H[0, 1, x])/3) - (64*(-1 + x)*H[0, -1, -1, x])/3 - + 64*H[0, -1, 1, x] + (16*(-43 + 13*x)*H[0, 0, -1, x])/3 + + (32*(17 + 12*x)*H[0, 0, 1, x])/3 - 64*H[0, 1, -1, x] - + (80*(1 + x)*H[0, 1, 1, x])/3) + + H[0, 1, x]*((-2*(-1431 - 19960*x + 70276*x^2 - 75515*x^3 + 25388*x^4 + 324*x^5))/(81*(-1 + x)^2*x) - 3072*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - 3072*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1)}, x] + 64*(-1 + x)*H[0, -1, -1, x] + - (160*(7 + x)*H[0, 0, -1, x])/3 - (64*(17 + 2*x)*H[0, 0, 1, x])/3 + - 64*(1 + x)*H[0, 1, -1, x] + (176*(1 + x)*H[0, 1, 1, x])/3) - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] + 64*(-1 + x)*H[0, -1, -1, x] + + (160*(7 + x)*H[0, 0, -1, x])/3 - (64*(17 + 2*x)*H[0, 0, 1, x])/3 + + 64*(1 + x)*H[0, 1, -1, x] + (176*(1 + x)*H[0, 1, 1, x])/3) - (32*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)*H[0, -1, -1, -1, x])/ (9*x*(1 + x)) + (32*(1 + x)*(14 + 43*x + 14*x^2)*H[0, -1, -1, 1, x])/ (9*x) - (16*(28 + 150*x - 363*x^2 - 156*x^3 + 339*x^4 + 18*x^5)* - H[0, -1, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + - (32*(1 + x)*(14 + 43*x + 14*x^2)*H[0, -1, 1, -1, x])/(9*x) - - (128*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) - + H[0, -1, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + + (32*(1 + x)*(14 + 43*x + 14*x^2)*H[0, -1, 1, -1, x])/(9*x) - + (128*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) - (16*(66 + 128*x + 75*x^2 + 49*x^3 + 28*x^4)*H[0, 0, -1, -1, x])/ (9*x*(1 + x)) + (16*(22 + 3*x - 59*x^2 + 10*x^3)*H[0, 0, -1, 1, x])/ (3*x) - (8*(-116 + 317*x - 861*x^2 - 687*x^3 + 667*x^4 + 200*x^5)* - H[0, 0, 0, -1, x])/(9*(-1 + x)*x*(1 + x)) + + H[0, 0, 0, -1, x])/(9*(-1 + x)*x*(1 + x)) + (16*(22 - 157*x - 953*x^2 - 8*x^3 + 824*x^4 + 86*x^5)*H[0, 0, 0, 1, x])/ - (9*(-1 + x)*x*(1 + x)) + - H[1, x]*((-2*(1080 + 13157*x - 14191*x^2 - 33994*x^3 - 39006*x^4 + - 241128*x^5 - 240696*x^6 + 73440*x^7))/(81*(-1 + x)*x) + - (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + - (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - - (8*(-1 + x)*(-10 + 5*x - 15*x^2 + 12*x^3)*H[0, -1, x])/(3*x^2) + - 32*(-1 + x)*H[0, -1, x]^2 + (4*(-60 + 6*x - 967*x^2 + 2194*x^3 - - 1251*x^4 + 48*x^5)*H[0, 1, x])/(9*(-1 + x)*x^2) - - (64*(70 - 135*x + 65*x^2 + 4*x^3)*H[0, 0, -1, x])/(9*(-1 + x)) + + (9*(-1 + x)*x*(1 + x)) + + H[1, x]*((-2*(1080 + 13157*x - 14191*x^2 - 33994*x^3 - 39006*x^4 + + 241128*x^5 - 240696*x^6 + 73440*x^7))/(81*(-1 + x)*x) + + (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (512*(-33 + 29*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (8*(-1 + x)*(-10 + 5*x - 15*x^2 + 12*x^3)*H[0, -1, x])/(3*x^2) + + 32*(-1 + x)*H[0, -1, x]^2 + (4*(-60 + 6*x - 967*x^2 + 2194*x^3 - + 1251*x^4 + 48*x^5)*H[0, 1, x])/(9*(-1 + x)*x^2) - + (64*(70 - 135*x + 65*x^2 + 4*x^3)*H[0, 0, -1, x])/(9*(-1 + x)) + (16*(-26 + 268*x - 429*x^2 + 189*x^3 + 6*x^4)*H[0, 0, 1, x])/ (9*(-1 + x)*x) - (16*(6 - 46*x + 83*x^2 - 43*x^3 + 2*x^4)* - H[0, 1, 1, x])/(3*(-1 + x)*x) + 384*(-1 + x)*H[0, 0, 0, -1, x] - - 288*(-1 + x)*H[0, 0, 0, 1, x]) + + H[0, 1, 1, x])/(3*(-1 + x)*x) + 384*(-1 + x)*H[0, 0, 0, -1, x] - + 288*(-1 + x)*H[0, 0, 0, 1, x]) + H[-1, x]*((-8*(-10 + 27*x + 96*x^2 + 63*x^3 + 8*x^4)*H[0, x]^3)/ (27*x*(1 + x)) - (8*(-90 - 161*x - 216*x^2 - 45*x^3 + 28*x^4)* H[0, -1, x])/(27*x^2) - (8*(1 + x)*(90 + 127*x - 175*x^2 + 136*x^3)* - H[0, 1, x])/(27*x^2) - 32*(1 + x)*H[0, 1, x]^2 + - H[0, x]^2*((2*(270 + 277*x + 1524*x^2 + 1485*x^3 + 88*x^4))/(27*x^2) + + H[0, 1, x])/(27*x^2) - 32*(1 + x)*H[0, 1, x]^2 + + H[0, x]^2*((2*(270 + 277*x + 1524*x^2 + 1485*x^3 + 88*x^4))/(27*x^2) + 16*(1 + x)*H[0, 1, x]) + (32*(4 + 69*x + 123*x^2 + 68*x^3 + 2*x^4)* H[0, -1, -1, x])/(9*x*(1 + x)) - (32*(1 + x)*(14 + 43*x + 14*x^2)* H[0, -1, 1, x])/(9*x) + (16*(66 + 128*x + 75*x^2 + 49*x^3 + 28*x^4)* H[0, 0, -1, x])/(9*x*(1 + x)) - (16*(22 + 3*x - 11*x^2 + 10*x^3)* H[0, 0, 1, x])/(3*x) - (32*(1 + x)*(14 + 43*x + 14*x^2)* - H[0, 1, -1, x])/(9*x) + (128*(1 + x)^3*H[0, 1, 1, x])/(9*x) + + H[0, 1, -1, x])/(9*x) + (128*(1 + x)^3*H[0, 1, 1, x])/(9*x) + H[0, x]*((16*(927 + 5978*x + 8862*x^2 + 4340*x^3 + 81*x^4))/ (81*x*(1 + x)) + (8*(-1 + x)*(-10 + 5*x - 15*x^2 + 12*x^3)*H[1, x])/ - (3*x^2) - (16*(44 + 11*x - 11*x^2 + 28*x^3)*H[0, -1, x])/(9*x) + - (16*(22 - 21*x - 42*x^2 + 4*x^3)*H[0, 1, x])/(9*x) - - 32*(1 + x)*H[0, 0, 1, x] + 64*(1 + x)*H[0, 1, 1, x]) - + (3*x^2) - (16*(44 + 11*x - 11*x^2 + 28*x^3)*H[0, -1, x])/(9*x) + + (16*(22 - 21*x - 42*x^2 + 4*x^3)*H[0, 1, x])/(9*x) - + 32*(1 + x)*H[0, 0, 1, x] + 64*(1 + x)*H[0, 1, 1, x]) - 32*(1 + x)*H[0, 0, 0, 1, x]) + (16*(22 + 3*x - 11*x^2 + 10*x^3)* - H[0, 0, 1, -1, x])/(3*x) - + H[0, 0, 1, -1, x])/(3*x) - (16*(26 - 32*x - 297*x^2 + 16*x^3 + 281*x^4 + 42*x^5)*H[0, 0, 1, 1, x])/ (9*(-1 + x)*x*(1 + x)) + (32*(1 + x)*(14 + 43*x + 14*x^2)* - H[0, 1, -1, -1, x])/(9*x) - (128*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) - - (128*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + + H[0, 1, -1, -1, x])/(9*x) - (128*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) - + (128*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) + (8*(132 - 487*x + 684*x^2 - 353*x^3 + 44*x^4)*H[0, 1, 1, 1, x])/ (9*(-1 + x)*x) + H[0, x]* - ((-2*(360 - 1405*x - 12835*x^2 + 2628*x^3 - 13002*x^4 + 80376*x^5 - - 80232*x^6 + 24480*x^7))/(27*(-1 + x)*x) + - 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + + ((-2*(360 - 1405*x - 12835*x^2 + 2628*x^3 - 13002*x^4 + 80376*x^5 - + 80232*x^6 + 24480*x^7))/(27*(-1 + x)*x) + + 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + 3072*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + - 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + - (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + - (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - - (2*(36 + 341*x - 399*x^2 + 24*x^3)*H[1, x]^2)/(9*x) + - (4*(12 - 81*x + 123*x^2 - 80*x^3 + 10*x^4)*H[1, x]^3)/(27*(-1 + x)*x) + - (16*(5 + 9*x^2)*H[-1, 1, x])/x - (128*(-1 + x)*H[0, -1, x]^2)/3 - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + + 1536*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + + (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (512*(-41 + 17*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (2*(36 + 341*x - 399*x^2 + 24*x^3)*H[1, x]^2)/(9*x) + + (4*(12 - 81*x + 123*x^2 - 80*x^3 + 10*x^4)*H[1, x]^3)/(27*(-1 + x)*x) + + (16*(5 + 9*x^2)*H[-1, 1, x])/x - (128*(-1 + x)*H[0, -1, x]^2)/3 - (4*(90 - 531*x - 862*x^2 + 1601*x^3 + 422*x^4 - 1276*x^5 + 216*x^6)* H[0, 1, x])/(27*(-1 + x)*x^2*(1 + x)) + (8*(41 + 5*x)*H[0, 1, x]^2)/ - 3 + H[0, -1, x]*((-4*(-270 + 11*x + 226*x^2 - 3164*x^3 + 168*x^4 + - 3421*x^5 + 72*x^6))/(27*(-1 + x)*x^2*(1 + x)) + - (64*(-11 + x)*H[0, 1, x])/3) + + 3 + H[0, -1, x]*((-4*(-270 + 11*x + 226*x^2 - 3164*x^3 + 168*x^4 + + 3421*x^5 + 72*x^6))/(27*(-1 + x)*x^2*(1 + x)) + + (64*(-11 + x)*H[0, 1, x])/3) + (16*(-82 + 3*x + 202*x^2 - 63*x^3 - 152*x^4 + 32*x^5)*H[0, -1, -1, x])/ (9*(-1 + x)*x*(1 + x)) - (16*(-22 + 213*x - 243*x^2 + 48*x^3 + 12*x^4)* - H[0, -1, 1, x])/(9*(-1 + x)*x) + + H[0, -1, 1, x])/(9*(-1 + x)*x) + (16*(-42 + 159*x - 33*x^2 - 274*x^3 - 12*x^4 + 64*x^5)*H[0, 0, -1, x])/ - (9*(-1 + x)*x*(1 + x)) - (8*(44 - 113*x - 970*x^2 - 11*x^3 + 846*x^4 + - 84*x^5)*H[0, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + + (9*(-1 + x)*x*(1 + x)) - (8*(44 - 113*x - 970*x^2 - 11*x^3 + 846*x^4 + + 84*x^5)*H[0, 0, 1, x])/(9*(-1 + x)*x*(1 + x)) + H[1, x]*((2*(2511 - 9631*x + 7671*x^2 - 4153*x^3 + 162*x^4))/ (81*(-1 + x)*x) + (32*(70 - 135*x + 65*x^2 + 4*x^3)*H[0, -1, x])/ (9*(-1 + x)) - (8*(52 + 218*x - 507*x^2 + 255*x^3 + 38*x^4)* - H[0, 1, x])/(9*(-1 + x)*x) - 64*(-1 + x)*H[0, -1, -1, x] - - 224*(-1 + x)*H[0, 0, -1, x] + 128*(-1 + x)*H[0, 0, 1, x]) - + H[0, 1, x])/(9*(-1 + x)*x) - 64*(-1 + x)*H[0, -1, -1, x] - + 224*(-1 + x)*H[0, 0, -1, x] + 128*(-1 + x)*H[0, 0, 1, x]) - (16*(-22 + 213*x - 315*x^2 + 120*x^3 + 12*x^4)*H[0, 1, -1, x])/ (9*(-1 + x)*x) + (8*(52 + 562*x - 337*x^2 - 540*x^3 + 283*x^4 + 56*x^5)* - H[0, 1, 1, x])/(9*(-1 + x)*x*(1 + x)) - - (256*(-1 + x)*H[0, -1, -1, -1, x])/3 + 64*(-1 + x)*H[0, -1, -1, 1, x] + - (32*(17 + 3*x)*H[0, -1, 0, 1, x])/3 + 64*(-1 + x)*H[0, -1, 1, -1, x] - - 64*(1 + x)*H[0, -1, 1, 1, x] + (64*(-8 + 5*x)*H[0, 0, -1, -1, x])/3 + + H[0, 1, 1, x])/(9*(-1 + x)*x*(1 + x)) - + (256*(-1 + x)*H[0, -1, -1, -1, x])/3 + 64*(-1 + x)*H[0, -1, -1, 1, x] + + (32*(17 + 3*x)*H[0, -1, 0, 1, x])/3 + 64*(-1 + x)*H[0, -1, 1, -1, x] - + 64*(1 + x)*H[0, -1, 1, 1, x] + (64*(-8 + 5*x)*H[0, 0, -1, -1, x])/3 + (128*(8 + 5*x)*H[0, 0, -1, 1, x])/3 - (32*(64 + x)*H[0, 0, 0, -1, x])/ 3 + 16*(27 + 35*x)*H[0, 0, 0, 1, x] + (128*(8 + 5*x)*H[0, 0, 1, -1, x])/ - 3 - (176*(3 + 5*x)*H[0, 0, 1, 1, x])/3 + - 64*(-1 + x)*H[0, 1, -1, -1, x] - 64*(1 + x)*H[0, 1, -1, 1, x] - - 64*(1 + x)*H[0, 1, 1, -1, x] + (32*(1 + x)*H[0, 1, 1, 1, x])/3) - - (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 - - (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + - 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] - - (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - - (32*(-23 + 17*x)*H[0, 0, -1, 0, -1, x])/3 + - (32*(-55 + 9*x)*H[0, 0, -1, 0, 1, x])/3 + - 128*(1 + x)*H[0, 0, -1, 1, 1, x] - 32*(-23 + 17*x)*H[0, 0, 0, -1, -1, x] - - 32*(45 + 11*x)*H[0, 0, 0, -1, 1, x] + - (64*(59 + 26*x)*H[0, 0, 0, 0, -1, x])/3 - - (16*(137 + 213*x)*H[0, 0, 0, 0, 1, x])/3 - - 32*(45 + 11*x)*H[0, 0, 0, 1, -1, x] + 80*(21 + 11*x)*H[0, 0, 0, 1, 1, x] - - (64*(23 + 6*x)*H[0, 0, 1, 0, -1, x])/3 + - (32*(68 + 21*x)*H[0, 0, 1, 0, 1, x])/3 - - 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - - 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + - CF^2*TF*((448*B4)/3 - (16*(180 + 2181*x - 7221*x^2 + 7404*x^3 - 4232*x^4 + - 960*x^5))/(27*x) - (32*(137 + 5*x)*z5)/3 - - 3072*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 - - (1024*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/3 + + 3 - (176*(3 + 5*x)*H[0, 0, 1, 1, x])/3 + + 64*(-1 + x)*H[0, 1, -1, -1, x] - 64*(1 + x)*H[0, 1, -1, 1, x] - + 64*(1 + x)*H[0, 1, 1, -1, x] + (32*(1 + x)*H[0, 1, 1, 1, x])/3) - + (256*(-1 + x)*H[0, -1, -1, 0, 1, x])/3 - + (512*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + 64*(1 + x)*H[0, -1, 0, 1, 1, x] + 64*(1 + x)*H[0, -1, 1, 0, 1, x] - + (1024*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 - + (32*(-23 + 17*x)*H[0, 0, -1, 0, -1, x])/3 + + (32*(-55 + 9*x)*H[0, 0, -1, 0, 1, x])/3 + + 128*(1 + x)*H[0, 0, -1, 1, 1, x] - 32*(-23 + 17*x)*H[0, 0, 0, -1, -1, x] - + 32*(45 + 11*x)*H[0, 0, 0, -1, 1, x] + + (64*(59 + 26*x)*H[0, 0, 0, 0, -1, x])/3 - + (16*(137 + 213*x)*H[0, 0, 0, 0, 1, x])/3 - + 32*(45 + 11*x)*H[0, 0, 0, 1, -1, x] + 80*(21 + 11*x)*H[0, 0, 0, 1, 1, x] - + (64*(23 + 6*x)*H[0, 0, 1, 0, -1, x])/3 + + (32*(68 + 21*x)*H[0, 0, 1, 0, 1, x])/3 - + 128*(1 + x)*H[0, 0, 1, 1, -1, x] - (1120*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 64*(1 + x)*H[0, 1, 0, 1, -1, x] - (464*(1 + x)*H[0, 1, 0, 1, 1, x])/3) + + CF^2*TF*((448*B4)/3 - (16*(180 + 2181*x - 7221*x^2 + 7404*x^3 - 4232*x^4 + + 960*x^5))/(27*x) - (32*(137 + 5*x)*z5)/3 - + 3072*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 - + (1024*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - - 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* - ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - VarGL^(-1)}, x] - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1)}, x]) + - (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(3*x^2) + - (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(3*x^2) + - (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + - (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + - (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + ((-512*Sqrt[1 - x]*(-40 + 277*x - 372*x^2 + 120*x^3))/(9*Sqrt[x]) - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + VarGL^(-1)}, x] - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1)}, x]) + + (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/(3*x^2) + + (2048*(-5 + 12*x - 42*x^2 + 20*x^3)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/(3*x^2) + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 + + (28672*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] + 12288*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + - (256*(1 + x)*H[-1, x]^3*H[0, x])/3 - (2*(-7 + 3*x)*H[0, x]^4)/9 + - (2*(1 + x)*H[0, x]^5)/15 + z4*((20*(-277 + 27*x))/3 - - (16*(109 + 61*x)*H[0, x])/3) - (164*(-1 + x)*H[1, x]^3)/9 - - (10*(-1 + x)*H[1, x]^4)/9 + (32*(10 + 23*x)*H[0, -1, x]^2)/3 + - H[-1, x]^2*((-16*(1 + x)*(10 + 14*x + 33*x^2)*H[0, x])/(3*x^2) - - (320*(1 + x)*H[0, x]^2)/3 - 256*(1 + x)*H[0, -1, x]) - - (16*(-41 + 17*x)*H[0, 1, x]^2)/3 + - H[1, x]^2*((-692*(-1 + x))/3 - (16*(-1 + x)*H[0, 1, x])/3) + - z3*((-4*(147 - 167*x + 24*x^2))/3 - 384*(1 + x)*H[-1, x] + - (16*(-196 + 13*x)*H[0, x])/3 - (8*(-1 + 15*x)*H[0, x]^2)/3 - - (16*(-1 + x)*H[1, x])/3 + 192*(-1 + x)*H[0, -1, x] - - (32*(1 + x)*H[0, 1, x])/3) + H[0, x]^3*((-2*(5 + x)*(7 + 16*x))/9 - - (208*(-1 + x)*H[1, x])/9 + (64*(-1 + x)*H[0, -1, x])/9 + + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] + + (256*(1 + x)*H[-1, x]^3*H[0, x])/3 - (2*(-7 + 3*x)*H[0, x]^4)/9 + + (2*(1 + x)*H[0, x]^5)/15 + z4*((20*(-277 + 27*x))/3 - + (16*(109 + 61*x)*H[0, x])/3) - (164*(-1 + x)*H[1, x]^3)/9 - + (10*(-1 + x)*H[1, x]^4)/9 + (32*(10 + 23*x)*H[0, -1, x]^2)/3 + + H[-1, x]^2*((-16*(1 + x)*(10 + 14*x + 33*x^2)*H[0, x])/(3*x^2) - + (320*(1 + x)*H[0, x]^2)/3 - 256*(1 + x)*H[0, -1, x]) - + (16*(-41 + 17*x)*H[0, 1, x]^2)/3 + + H[1, x]^2*((-692*(-1 + x))/3 - (16*(-1 + x)*H[0, 1, x])/3) + + z3*((-4*(147 - 167*x + 24*x^2))/3 - 384*(1 + x)*H[-1, x] + + (16*(-196 + 13*x)*H[0, x])/3 - (8*(-1 + 15*x)*H[0, x]^2)/3 - + (16*(-1 + x)*H[1, x])/3 + 192*(-1 + x)*H[0, -1, x] - + (32*(1 + x)*H[0, 1, x])/3) + H[0, x]^3*((-2*(5 + x)*(7 + 16*x))/9 - + (208*(-1 + x)*H[1, x])/9 + (64*(-1 + x)*H[0, -1, x])/9 + (32*(1 + x)*H[0, 1, x])/3) - (32*(1 + x)*(10 + 14*x + 33*x^2)* H[0, -1, -1, x])/(3*x^2) + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)* H[0, -1, 1, x])/(3*x^2) + (16*(30 + 96*x + 153*x^2 + 175*x^3)* H[0, 0, -1, x])/(3*x^2) + (8*(-20 + 56*x + 47*x^2 + 163*x^3 + 64*x^4)* H[0, 0, 1, x])/(3*x^2) + H[0, -1, x]* ((-32*(1 + x)*(97 + 35*x + 19*x^2))/(9*x) + (256*(-5 + 3*x)*H[0, 1, x])/ - 3 + 256*(-1 + x)*H[0, -1, -1, x] + 128*(-1 + x)*H[0, 0, -1, x] - - 256*(-1 + x)*H[0, 0, 1, x]) + - H[-1, x]*((8*(1 + x)*(30 + 50*x + 103*x^2 + 8*x^3)*H[0, x]^2)/(3*x^2) - + 3 + 256*(-1 + x)*H[0, -1, -1, x] + 128*(-1 + x)*H[0, 0, -1, x] - + 256*(-1 + x)*H[0, 0, 1, x]) + + H[-1, x]*((8*(1 + x)*(30 + 50*x + 103*x^2 + 8*x^3)*H[0, x]^2)/(3*x^2) - (128*(1 + x)*H[0, x]^3)/9 + (32*(1 + x)*(10 + 14*x + 33*x^2)* H[0, -1, x])/(3*x^2) - (64*(1 + x)*(5 + 10*x + 19*x^2 + 3*x^3)* H[0, 1, x])/(3*x^2) + H[0, x]*((32*(1 + x)*(97 + 35*x + 19*x^2))/ - (9*x) + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[1, x])/(3*x^2) + - (1024*(1 + x)*H[0, -1, x])/3 - 256*(1 + x)*H[0, 1, x]) + - 512*(1 + x)*H[0, -1, -1, x] - 256*(1 + x)*H[0, 0, -1, x] + + (9*x) + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[1, x])/(3*x^2) + + (1024*(1 + x)*H[0, -1, x])/3 - 256*(1 + x)*H[0, 1, x]) + + 512*(1 + x)*H[0, -1, -1, x] - 256*(1 + x)*H[0, 0, -1, x] + 512*(1 + x)*H[0, 0, 1, x]) + (64*(1 + x)*(5 + 10*x + 19*x^2 + 3*x^3)* H[0, 1, -1, x])/(3*x^2) - (32*(20 - 48*x + 60*x^2 - 65*x^3 + 6*x^4)* - H[0, 1, 1, x])/(3*x^2) + - H[1, x]*((-8*(-1 + x)*(120 - 1785*x - 2536*x^2 + 8176*x^3 - 7312*x^4 + - 1920*x^5))/(9*x) + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + + H[0, 1, 1, x])/(3*x^2) + + H[1, x]*((-8*(-1 + x)*(120 - 1785*x - 2536*x^2 + 8176*x^3 - 7312*x^4 + + 1920*x^5))/(9*x) + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + 6144*(-1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1)}, x] - - (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[0, -1, x])/(3*x^2) + - (16*(20 - 48*x + 107*x^2 - 79*x^3 + 8*x^4)*H[0, 1, x])/(3*x^2) - - 512*(-1 + x)*H[0, 0, -1, x] + 96*(-1 + x)*H[0, 0, 1, x] + - (416*(-1 + x)*H[0, 1, 1, x])/3) + - H[0, x]^2*((-2*(240 + 1593*x + 1835*x^2 + 152*x^3))/(9*x) - + Sqrt[VarGL], VarGL^(-1)}, x] - + (64*(-1 + x)*(-5 + 10*x - 19*x^2 + 3*x^3)*H[0, -1, x])/(3*x^2) + + (16*(20 - 48*x + 107*x^2 - 79*x^3 + 8*x^4)*H[0, 1, x])/(3*x^2) - + 512*(-1 + x)*H[0, 0, -1, x] + 96*(-1 + x)*H[0, 0, 1, x] + + (416*(-1 + x)*H[0, 1, 1, x])/3) + + H[0, x]^2*((-2*(240 + 1593*x + 1835*x^2 + 152*x^3))/(9*x) - 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1)}, x] - - (4*(-1 + x)*(-20 + 36*x + 13*x^2 + 8*x^3)*H[1, x])/(3*x^2) + - 8*(-1 + x)*H[1, x]^2 + (16*(38 + 51*x)*H[0, -1, x])/3 + - (16*(-15 + 32*x)*H[0, 1, x])/3 + (320*(-1 + x)*H[0, -1, -1, x])/3 - - (256*(-3 + 2*x)*H[0, 0, -1, x])/3 - (16*(31 + 23*x)*H[0, 0, 1, x])/3 - - (32*(1 + x)*H[0, 1, 1, x])/3) + - H[0, 1, x]*((-8*(474 - 183*x + 1405*x^2))/(9*x) - + Sqrt[VarGL], VarGL^(-1)}, x] - + (4*(-1 + x)*(-20 + 36*x + 13*x^2 + 8*x^3)*H[1, x])/(3*x^2) + + 8*(-1 + x)*H[1, x]^2 + (16*(38 + 51*x)*H[0, -1, x])/3 + + (16*(-15 + 32*x)*H[0, 1, x])/3 + (320*(-1 + x)*H[0, -1, -1, x])/3 - + (256*(-3 + 2*x)*H[0, 0, -1, x])/3 - (16*(31 + 23*x)*H[0, 0, 1, x])/3 - + (32*(1 + x)*H[0, 1, 1, x])/3) + + H[0, 1, x]*((-8*(474 - 183*x + 1405*x^2))/(9*x) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1)}, x] - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1)}, x] + 256*(1 + x)*H[0, 0, -1, x] - - (448*(1 + x)*H[0, 0, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, x])/3) + - z2*((2*(480 + 909*x + 7507*x^2 + 304*x^3))/(9*x) - 16*(13 + 5*x)*z3 + - 128*(1 + x)*H[-1, x]^2 - (4*(103 + 17*x)*H[0, x]^2)/3 + + Sqrt[VarGL], VarGL^(-1)}, x] + 256*(1 + x)*H[0, 0, -1, x] - + (448*(1 + x)*H[0, 0, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, x])/3) + + z2*((2*(480 + 909*x + 7507*x^2 + 304*x^3))/(9*x) - 16*(13 + 5*x)*z3 + + 128*(1 + x)*H[-1, x]^2 - (4*(103 + 17*x)*H[0, x]^2)/3 + (4*(1 + x)*H[0, x]^3)/9 + H[-1, x]* - ((-16*(1 + x)*(20 + 34*x + 71*x^2 + 6*x^3))/(3*x^2) + + ((-16*(1 + x)*(20 + 34*x + 71*x^2 + 6*x^3))/(3*x^2) + (256*(1 + x)*H[0, x])/3) + (4*(-24 + 131*x - 147*x^2 + 8*x^3)*H[1, x])/ - (3*x) - 84*(-1 + x)*H[1, x]^2 - (160*(6 + 7*x)*H[0, -1, x])/3 - - (8*(5 + 23*x)*H[0, 1, x])/3 + H[0, x]*((-2*(265 + 701*x))/3 - - (176*(-1 + x)*H[1, x])/3 - (128*(-1 + x)*H[0, -1, x])/3 + - 32*(1 + x)*H[0, 1, x]) - 128*(-1 + x)*H[0, -1, -1, x] + - 128*(-3 + 2*x)*H[0, 0, -1, x] + (32*(13 + x)*H[0, 0, 1, x])/3 + - (176*(1 + x)*H[0, 1, 1, x])/3) - 512*(1 + x)*H[0, -1, -1, -1, x] - - 512*x*H[0, -1, 0, 1, x] + 256*(1 + x)*H[0, 0, -1, -1, x] - - 512*(1 + x)*H[0, 0, -1, 1, x] + (32*(98 + 23*x)*H[0, 0, 0, -1, x])/3 + - 96*(-1 + 6*x)*H[0, 0, 0, 1, x] - 512*(1 + x)*H[0, 0, 1, -1, x] + + (3*x) - 84*(-1 + x)*H[1, x]^2 - (160*(6 + 7*x)*H[0, -1, x])/3 - + (8*(5 + 23*x)*H[0, 1, x])/3 + H[0, x]*((-2*(265 + 701*x))/3 - + (176*(-1 + x)*H[1, x])/3 - (128*(-1 + x)*H[0, -1, x])/3 + + 32*(1 + x)*H[0, 1, x]) - 128*(-1 + x)*H[0, -1, -1, x] + + 128*(-3 + 2*x)*H[0, 0, -1, x] + (32*(13 + x)*H[0, 0, 1, x])/3 + + (176*(1 + x)*H[0, 1, 1, x])/3) - 512*(1 + x)*H[0, -1, -1, -1, x] - + 512*x*H[0, -1, 0, 1, x] + 256*(1 + x)*H[0, 0, -1, -1, x] - + 512*(1 + x)*H[0, 0, -1, 1, x] + (32*(98 + 23*x)*H[0, 0, 0, -1, x])/3 + + 96*(-1 + 6*x)*H[0, 0, 0, 1, x] - 512*(1 + x)*H[0, 0, 1, -1, x] + (160*(-3 + 7*x)*H[0, 0, 1, 1, x])/3 - (16*(-67 + 53*x)*H[0, 1, 1, 1, x])/ - 3 + H[0, x]*((-8*(-120 + 973*x + 880*x^2 - 10712*x^3 + 15488*x^4 - + 3 + H[0, x]*((-8*(-120 + 973*x + 880*x^2 - 10712*x^3 + 15488*x^4 - 9232*x^5 + 1920*x^6))/(9*x) + 2048*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2 + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + - 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + - (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + - (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - - (8*(-1 + x)*(-13 + 4*x)*H[1, x]^2)/3 - (176*(-1 + x)*H[1, x]^3)/9 + - (128*(15 + 22*x^2)*H[-1, 1, x])/(3*x) - (256*(-1 + x)*H[0, -1, x]^2)/3 - - (16*(-10 + 28*x - 4*x^2 + 21*x^3 + 12*x^4)*H[0, 1, x])/(3*x^2) + - 32*(1 + x)*H[0, 1, x]^2 + H[1, x]*((-8*(-1 + x)*(118 + 47*x))/(3*x) + - 256*(-1 + x)*H[0, -1, x] - 32*(-1 + x)*H[0, 1, x]) + - H[0, -1, x]*((-16*(30 + 88*x + 153*x^2 + 143*x^3 + 4*x^4))/(3*x^2) - - 128*(1 + x)*H[0, 1, x]) - (832*(2 + 3*x)*H[0, -1, -1, x])/3 + - (2048*H[0, -1, 1, x])/3 - (128*(17 + 14*x)*H[0, 0, -1, x])/3 - - 32*(-8 + 15*x)*H[0, 0, 1, x] + (2048*H[0, 1, -1, x])/3 - - (128*(3 + x)*H[0, 1, 1, x])/3 - 256*(-1 + x)*H[0, -1, -1, -1, x] + - 256*x*H[0, -1, 0, 1, x] + 256*(-1 + x)*H[0, 0, -1, -1, x] + - 256*(2 + x)*H[0, 0, -1, 1, x] + 128*(-11 + 5*x)*H[0, 0, 0, -1, x] + - 256*(3 + 2*x)*H[0, 0, 0, 1, x] + 256*(2 + x)*H[0, 0, 1, -1, x] - - (256*(1 + x)*H[0, 0, 1, 1, x])/3 + 64*(1 + x)*H[0, 1, 1, 1, x]) - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + + 2048*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 + + (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 + + (2048*(-23 + 9*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 - + (8*(-1 + x)*(-13 + 4*x)*H[1, x]^2)/3 - (176*(-1 + x)*H[1, x]^3)/9 + + (128*(15 + 22*x^2)*H[-1, 1, x])/(3*x) - (256*(-1 + x)*H[0, -1, x]^2)/3 - + (16*(-10 + 28*x - 4*x^2 + 21*x^3 + 12*x^4)*H[0, 1, x])/(3*x^2) + + 32*(1 + x)*H[0, 1, x]^2 + H[1, x]*((-8*(-1 + x)*(118 + 47*x))/(3*x) + + 256*(-1 + x)*H[0, -1, x] - 32*(-1 + x)*H[0, 1, x]) + + H[0, -1, x]*((-16*(30 + 88*x + 153*x^2 + 143*x^3 + 4*x^4))/(3*x^2) - + 128*(1 + x)*H[0, 1, x]) - (832*(2 + 3*x)*H[0, -1, -1, x])/3 + + (2048*H[0, -1, 1, x])/3 - (128*(17 + 14*x)*H[0, 0, -1, x])/3 - + 32*(-8 + 15*x)*H[0, 0, 1, x] + (2048*H[0, 1, -1, x])/3 - + (128*(3 + x)*H[0, 1, 1, x])/3 - 256*(-1 + x)*H[0, -1, -1, -1, x] + + 256*x*H[0, -1, 0, 1, x] + 256*(-1 + x)*H[0, 0, -1, -1, x] + + 256*(2 + x)*H[0, 0, -1, 1, x] + 128*(-11 + 5*x)*H[0, 0, 0, -1, x] + + 256*(3 + 2*x)*H[0, 0, 0, 1, x] + 256*(2 + x)*H[0, 0, 1, -1, x] - + (256*(1 + x)*H[0, 0, 1, 1, x])/3 + 64*(1 + x)*H[0, 1, 1, 1, x]) - 512*(-1 + x)*H[0, -1, 0, -1, -1, x] - 1024*(-1 + x)* - H[0, 0, -1, -1, -1, x] - 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - - 768*H[0, 0, -1, 0, 1, x] - 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - - 2304*H[0, 0, 0, -1, 1, x] - (2048*(-4 + x)*H[0, 0, 0, 0, -1, x])/3 - - (128*(31 + 19*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*H[0, 0, 0, 1, -1, x] + - (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*H[0, 0, 1, 0, -1, x] + - 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - - 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + + H[0, 0, -1, -1, -1, x] - 384*(-1 + x)*H[0, 0, -1, 0, -1, x] - + 768*H[0, 0, -1, 0, 1, x] - 1152*(-1 + x)*H[0, 0, 0, -1, -1, x] - + 2304*H[0, 0, 0, -1, 1, x] - (2048*(-4 + x)*H[0, 0, 0, 0, -1, x])/3 - + (128*(31 + 19*x)*H[0, 0, 0, 0, 1, x])/3 - 2304*H[0, 0, 0, 1, -1, x] + + (2560*(1 + x)*H[0, 0, 0, 1, 1, x])/3 - 768*H[0, 0, 1, 0, -1, x] + + 448*(1 + x)*H[0, 0, 1, 0, 1, x] - (704*(1 + x)*H[0, 0, 1, 1, 1, x])/3 - + 128*(1 + x)*H[0, 1, 0, 1, 1, x] + (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3) + CA*(TF^2*((8*(433567 + 493927*x - 565164*x^2 - 117720*x^3 + 138240*x^4))/ - 18225 - (16*(119 + 676*x)*z3)/45 + - (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + + 18225 - (16*(119 + 676*x)*z3)/45 + + (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + 61440*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/ - (675*(-((-1 + x)*x))^(3/2)) + - (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + + (675*(-((-1 + x)*x))^(3/2)) + + (8*(-49 - 2539*x - 75474*x^2 + 162796*x^3 - 31664*x^4 - 113760*x^5 + 61440*x^6)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/ - (675*(-((-1 + x)*x))^(3/2)) - - (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/45 - - (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/45 - - (16*(-35 + x)*H[0, x]^3)/405 - (8*(-143 + 178*x)*H[1, x]^2)/135 + - H[0, x]^2*((8*(-4250 - 1317*x + 5027*x^2))/(2025*(-1 + x)) - + (675*(-((-1 + x)*x))^(3/2)) - + (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/45 - + (512*(83 + 128*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/45 - + (16*(-35 + x)*H[0, x]^3)/405 - (8*(-143 + 178*x)*H[1, x]^2)/135 + + H[0, x]^2*((8*(-4250 - 1317*x + 5027*x^2))/(2025*(-1 + x)) - (32*x*H[1, x])/15) + z2*((-8*(17500 - 49809*x + 31229*x^2))/ - (2025*(-1 + x)) + (16*(145 + 217*x)*H[0, x])/135 + + (2025*(-1 + x)) + (16*(145 + 217*x)*H[0, x])/135 + (64*x*H[1, x])/15) + (8*(10165 - 29589*x + 18344*x^2)*H[0, 1, x])/ (2025*(-1 + x)) + H[1, x]* ((32*(-2963 - 8767*x + 38844*x^2 - 21144*x^3 - 15570*x^4 + 11520*x^5))/ - 2025 - (64*x*H[0, 1, x])/15) + - H[0, x]*((16*(-7674 + 25658*x - 96497*x^2 + 119976*x^3 - 11148*x^4 - - 54180*x^5 + 23040*x^6))/(2025*(-1 + x)) - - (8*(-491 + 471*x)*H[1, x])/135 + (8*(169 + 304*x)*H[0, 1, x])/135) - + 2025 - (64*x*H[0, 1, x])/15) + + H[0, x]*((16*(-7674 + 25658*x - 96497*x^2 + 119976*x^3 - 11148*x^4 - + 54180*x^5 + 23040*x^6))/(2025*(-1 + x)) - + (8*(-491 + 471*x)*H[1, x])/135 + (8*(169 + 304*x)*H[0, 1, x])/135) - (304*(11 + 20*x)*H[0, 0, 1, x])/135 + (8*(89 + 296*x)*H[0, 1, 1, x])/ - 135 + NF*((-8*(-24449 + 31393*x))/729 + (64*(-1 + 6*x)*z3)/9 - - (4*(-584 + 25*x)*H[0, x]^2)/81 + (224*(1 + x)*H[0, x]^3)/81 + - z2*((-40*(8 + 65*x))/81 - (32*(1 + x)*H[0, x])/27) - - (8*(-281 + 137*x)*H[1, x])/81 + (4*(-41 + 25*x)*H[1, x]^2)/27 + - (8*(85 + 232*x)*H[0, 1, x])/81 + - H[0, x]*((-8*(1220 - 1337*x + 177*x^2))/(81*(-1 + x)) - - (8*(-41 + 45*x)*H[1, x])/27 + (128*(1 + x)*H[0, 1, x])/27) - - (128*(1 + x)*H[0, 0, 1, x])/27 - (128*(1 + x)*H[0, 1, 1, x])/27)) + - CF*TF*(-96*B4*(1 + 2*x) + (4*(-6480 + 691055*x - 1544560*x^2 + - 762245*x^3 + 282708*x^4 - 279576*x^5 + 87264*x^6))/(243*(-1 + x)*x) + + 135 + NF*((-8*(-24449 + 31393*x))/729 + (64*(-1 + 6*x)*z3)/9 - + (4*(-584 + 25*x)*H[0, x]^2)/81 + (224*(1 + x)*H[0, x]^3)/81 + + z2*((-40*(8 + 65*x))/81 - (32*(1 + x)*H[0, x])/27) - + (8*(-281 + 137*x)*H[1, x])/81 + (4*(-41 + 25*x)*H[1, x]^2)/27 + + (8*(85 + 232*x)*H[0, 1, x])/81 + + H[0, x]*((-8*(1220 - 1337*x + 177*x^2))/(81*(-1 + x)) - + (8*(-41 + 45*x)*H[1, x])/27 + (128*(1 + x)*H[0, 1, x])/27) - + (128*(1 + x)*H[0, 0, 1, x])/27 - (128*(1 + x)*H[0, 1, 1, x])/27)) + + CF*TF*(-96*B4*(1 + 2*x) + (4*(-6480 + 691055*x - 1544560*x^2 + + 762245*x^3 + 282708*x^4 - 279576*x^5 + 87264*x^6))/(243*(-1 + x)*x) + (16*(883 + 111*x)*z5)/3 + (1024*(-21 + 19*x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2)/3 + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^2)/3 + (1024*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2)/ 3 + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]* ((-64*(320 - 985*x + 3701*x^2 - 5670*x^3 + 2592*x^4))/ (9*Sqrt[-((-1 + x)*x)]) + (2048*(-21 + 19*x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x]) + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]* ((-64*(320 - 985*x + 3701*x^2 - 5670*x^3 + 2592*x^4))/ (9*Sqrt[-((-1 + x)*x)]) + 8192*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x]) - (256*(40 - 94*x + 259*x^2 - 677*x^3 + 456*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + (1 - VarGL)^(-1)}, x])/(3*(-1 + x)*x^2) - (256*(40 - 94*x + 259*x^2 - 677*x^3 + 456*x^4)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1)}, x])/(3*(-1 + x)*x^2) - - (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x])/(3*(-1 + x)*x^2) - + (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 - + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x])/3 - (2048*(11 + 6*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 - - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - + Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x])/3 - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), (1 - VarGL)^(-1)}, x] - + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1), VarGL^(-1)}, x] - 16384*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1), (1 - VarGL)^(-1), VarGL^(-1)}, x] - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + + Sqrt[VarGL], (1 - VarGL)^(-1), VarGL^(-1), VarGL^(-1)}, x] + 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), (1 - VarGL)^(-1)}, x] - 24576*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]* - Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] - - (32*(1 + x)*(4 + 41*x + 4*x^2)*H[-1, x]^3*H[0, x])/(27*x) - - (4*(-190 - 49*x + 12*x^2)*H[0, x]^4)/27 - (4*(-9 + 5*x)*H[0, x]^5)/15 + - z4*((-4*(-10838 - 3563*x + 72*x^2))/9 + (8*(550 + 19*x)*H[0, x])/3) + - (532*(-1 + x)*H[1, x]^3)/27 + (10*(-1 + x)*H[1, x]^4)/9 + - (16*(38 + 87*x - 177*x^2 + 4*x^3)*H[0, -1, x]^2)/(9*x) - - (16*(-52 + 279*x - 114*x^2 + 10*x^3)*H[0, 1, x]^2)/(9*x) + - z3*((4*(11627 - 8151*x - 3648*x^2 + 604*x^3))/(27*(-1 + x)) - - (16*(1 + x)*(50 + 25*x + 32*x^2)*H[-1, x])/(9*x) + - (16*(373 - 104*x + 76*x^2)*H[0, x])/9 + (16*(-34 + 5*x)*H[0, x]^2)/3 + - (16*(68 - 147*x + 111*x^2 + 4*x^3)*H[1, x])/(9*x) - - (256*(-1 + x)*H[0, -1, x])/3 - (128*(1 + x)*H[0, 1, x])/3) + - H[0, x]^3*((4*(3755 - 1081*x + 52*x^2))/81 + - (8*(-1 + x)*(44 + 161*x + 8*x^2)*H[1, x])/(27*x) - - (176*(-1 + x)*H[0, -1, x])/9 - (208*(1 + x)*H[0, 1, x])/9) + + Sqrt[VarGL], VarGL^(-1), VarGL^(-1), VarGL^(-1)}, x] - + (32*(1 + x)*(4 + 41*x + 4*x^2)*H[-1, x]^3*H[0, x])/(27*x) - + (4*(-190 - 49*x + 12*x^2)*H[0, x]^4)/27 - (4*(-9 + 5*x)*H[0, x]^5)/15 + + z4*((-4*(-10838 - 3563*x + 72*x^2))/9 + (8*(550 + 19*x)*H[0, x])/3) + + (532*(-1 + x)*H[1, x]^3)/27 + (10*(-1 + x)*H[1, x]^4)/9 + + (16*(38 + 87*x - 177*x^2 + 4*x^3)*H[0, -1, x]^2)/(9*x) - + (16*(-52 + 279*x - 114*x^2 + 10*x^3)*H[0, 1, x]^2)/(9*x) + + z3*((4*(11627 - 8151*x - 3648*x^2 + 604*x^3))/(27*(-1 + x)) - + (16*(1 + x)*(50 + 25*x + 32*x^2)*H[-1, x])/(9*x) + + (16*(373 - 104*x + 76*x^2)*H[0, x])/9 + (16*(-34 + 5*x)*H[0, x]^2)/3 + + (16*(68 - 147*x + 111*x^2 + 4*x^3)*H[1, x])/(9*x) - + (256*(-1 + x)*H[0, -1, x])/3 - (128*(1 + x)*H[0, 1, x])/3) + + H[0, x]^3*((4*(3755 - 1081*x + 52*x^2))/81 + + (8*(-1 + x)*(44 + 161*x + 8*x^2)*H[1, x])/(27*x) - + (176*(-1 + x)*H[0, -1, x])/9 - (208*(1 + x)*H[0, 1, x])/9) + H[-1, x]^2*((-8*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, x])/ - (27*x^2) - (8*(1 + x)*(22 - x + 22*x^2)*H[0, x]^2)/(9*x) + - (32*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, x])/(9*x) - - (448*(1 + x)^3*H[0, 1, x])/(9*x)) + - H[1, x]^2*((4*(-1 + x)*(-477 - 74*x + 27*x^2))/(27*x) + - (16*(-2 - 33*x + 31*x^2 + 2*x^3)*H[0, 1, x])/(3*x)) - + (27*x^2) - (8*(1 + x)*(22 - x + 22*x^2)*H[0, x]^2)/(9*x) + + (32*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, x])/(9*x) - + (448*(1 + x)^3*H[0, 1, x])/(9*x)) + + H[1, x]^2*((4*(-1 + x)*(-477 - 74*x + 27*x^2))/(27*x) + + (16*(-2 - 33*x + 31*x^2 + 2*x^3)*H[0, 1, x])/(3*x)) - (16*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, -1, -1, x])/ (27*x^2) - (16*(180 - 323*x + 294*x^2 - 1101*x^3 + 190*x^4)* - H[0, -1, 1, x])/(27*x^2) - (8*(540 + 565*x + 1827*x^2 + 3546*x^3 + + H[0, -1, 1, x])/(27*x^2) - (8*(540 + 565*x + 1827*x^2 + 3546*x^3 + 56*x^4)*H[0, 0, -1, x])/(27*x^2) + H[0, -1, x]* - ((16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - - (64*(-37 + 34*x)*H[0, 1, x])/3 - (512*(-1 + x)*H[0, -1, -1, x])/3 + - (256*(-1 + x)*H[0, 0, -1, x])/3) - + ((16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - + (64*(-37 + 34*x)*H[0, 1, x])/3 - (512*(-1 + x)*H[0, -1, -1, x])/3 + + (256*(-1 + x)*H[0, 0, -1, x])/3) - (8*(180 - 1179*x - 11164*x^2 + 9321*x^3 + 1778*x^4 + 920*x^5)* - H[0, 0, 1, x])/(27*(-1 + x)*x^2) - - (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, -1, x])/(27*x^2) + + H[0, 0, 1, x])/(27*(-1 + x)*x^2) - + (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, -1, x])/(27*x^2) + (16*(-360 + 684*x - 2737*x^2 + 4797*x^3 - 2474*x^4 + 162*x^5)* - H[0, 1, 1, x])/(27*(-1 + x)*x^2) + - H[0, 1, x]*((8*(918 - 34900*x + 102373*x^2 - 103421*x^3 + 35084*x^4 + + H[0, 1, 1, x])/(27*(-1 + x)*x^2) + + H[0, 1, x]*((8*(918 - 34900*x + 102373*x^2 - 103421*x^3 + 35084*x^4 + 162*x^5))/(81*(-1 + x)^2*x) + 8192*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + 8192*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], - VarGL^(-1)}, x] - (1664*(1 + x)*H[0, 0, -1, x])/3 + - (1312*(1 + x)*H[0, 0, 1, x])/3 - 192*(1 + x)*H[0, 1, 1, x]) + + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + VarGL^(-1)}, x] - (1664*(1 + x)*H[0, 0, -1, x])/3 + + (1312*(1 + x)*H[0, 0, 1, x])/3 - 192*(1 + x)*H[0, 1, 1, x]) + z2*((-4*(2160 + 8377*x - 32965*x^2 + 34247*x^3 - 13205*x^4 + 1818*x^5))/ - (81*(-1 + x)^2*x) + (8*(19 + 17*x)*z3)/3 + - (16*(1 + x)*(8 + 5*x + 8*x^2)*H[-1, x]^2)/(3*x) + + (81*(-1 + x)^2*x) + (8*(19 + 17*x)*z3)/3 + + (16*(1 + x)*(8 + 5*x + 8*x^2)*H[-1, x]^2)/(3*x) + (8*(-148 + 155*x + 36*x^2)*H[0, x]^2)/9 - (8*(23 + 41*x)*H[0, x]^3)/ - 9 + H[-1, x]*((8*(1 + x)*(120 + 86*x + 163*x^2 + 26*x^3))/(9*x^2) - - (8*(1 + x)*(44 + 229*x + 80*x^2)*H[0, x])/(9*x)) - + 9 + H[-1, x]*((8*(1 + x)*(120 + 86*x + 163*x^2 + 26*x^3))/(9*x^2) - + (8*(1 + x)*(44 + 229*x + 80*x^2)*H[0, x])/(9*x)) - (4*(808 + 1079*x - 4854*x^2 + 2771*x^3 + 52*x^4)*H[1, x])/ (27*(-1 + x)*x) - (4*(-16 - 111*x + 87*x^2 + 16*x^3)*H[1, x]^2)/ - (9*x) - (8*(52 - 399*x - 411*x^2 + 64*x^3)*H[0, -1, x])/(9*x) + - (8*(-284 - 10*x + 623*x^2 + 72*x^3)*H[0, 1, x])/(9*x) + - H[0, x]*((28*(-767 - 941*x + 32*x^2))/27 - - (8*(-1 + x)*(84 + 179*x + 24*x^2)*H[1, x])/(3*x) + - (112*(-1 + x)*H[0, -1, x])/3 + (688*(1 + x)*H[0, 1, x])/3) + + (9*x) - (8*(52 - 399*x - 411*x^2 + 64*x^3)*H[0, -1, x])/(9*x) + + (8*(-284 - 10*x + 623*x^2 + 72*x^3)*H[0, 1, x])/(9*x) + + H[0, x]*((28*(-767 - 941*x + 32*x^2))/27 - + (8*(-1 + x)*(84 + 179*x + 24*x^2)*H[1, x])/(3*x) + + (112*(-1 + x)*H[0, -1, x])/3 + (688*(1 + x)*H[0, 1, x])/3) + (256*(-1 + x)*H[0, -1, -1, x])/3 - (32*(-55 + 19*x)*H[0, 0, -1, x])/ 3 - (16*(115 + 91*x)*H[0, 0, 1, x])/3 + (208*(1 + x)*H[0, 1, 1, x])/ - 3) + H[0, x]^2*((4*(-1080 - 11923*x - 9906*x^2 + 22243*x^3 + + 3) + H[0, x]^2*((4*(-1080 - 11923*x - 9906*x^2 + 22243*x^3 + 747*x^4))/(81*(-1 + x)*x) + 4096*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x] + 4096*(1 + x)* - GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], + GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] + (4*(20 - 63*x - 297*x^2 + 322*x^3 + 12*x^4)* H[1, x])/(3*x^2) - (4*(-1 + x)*(52 + 205*x + 16*x^2)*H[1, x]^2)/ - (9*x) + (16*(26 - 111*x - 189*x^2 + 22*x^3)*H[0, -1, x])/(9*x) - - (8*(-44 + 83*x + 686*x^2 + 24*x^3)*H[0, 1, x])/(9*x) - - 64*(-1 + x)*H[0, -1, -1, x] + (64*(-19 + 10*x)*H[0, 0, -1, x])/3 + - (32*(23 + 28*x)*H[0, 0, 1, x])/3 + (272*(1 + x)*H[0, 1, 1, x])/3) + + (9*x) + (16*(26 - 111*x - 189*x^2 + 22*x^3)*H[0, -1, x])/(9*x) - + (8*(-44 + 83*x + 686*x^2 + 24*x^3)*H[0, 1, x])/(9*x) - + 64*(-1 + x)*H[0, -1, -1, x] + (64*(-19 + 10*x)*H[0, 0, -1, x])/3 + + (32*(23 + 28*x)*H[0, 0, 1, x])/3 + (272*(1 + x)*H[0, 1, 1, x])/3) + H[-1, x]*((-4*(1 + x)*(540 + 457*x + 26*x^2 + 160*x^3)*H[0, x]^2)/ - (27*x^2) + (8*(1 + x)*(-20 + 179*x + 16*x^2)*H[0, x]^3)/(27*x) + - (16*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, -1, x])/(27*x^2) + - (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, x])/(27*x^2) + - H[0, x]*((-16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - - (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[1, x])/(3*x^2) + - (32*(1 + x)*(44 + 73*x + 26*x^2)*H[0, -1, x])/(9*x) - - (32*(1 + x)*(22 + 35*x + 4*x^2)*H[0, 1, x])/(9*x)) - - (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, x])/(9*x) + - (896*(1 + x)^3*H[0, -1, 1, x])/(9*x) - - (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, x])/(3*x) + - (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, x])/(3*x) + + (27*x^2) + (8*(1 + x)*(-20 + 179*x + 16*x^2)*H[0, x]^3)/(27*x) + + (16*(1 + x)*(-180 - 197*x + 968*x^2 + 28*x^3)*H[0, -1, x])/(27*x^2) + + (16*(1 + x)*(180 + 307*x - 13*x^2 + 190*x^3)*H[0, 1, x])/(27*x^2) + + H[0, x]*((-16*(1 + x)*(777 - 808*x + 138*x^2))/(27*x) - + (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[1, x])/(3*x^2) + + (32*(1 + x)*(44 + 73*x + 26*x^2)*H[0, -1, x])/(9*x) - + (32*(1 + x)*(22 + 35*x + 4*x^2)*H[0, 1, x])/(9*x)) - + (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, x])/(9*x) + + (896*(1 + x)^3*H[0, -1, 1, x])/(9*x) - + (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, x])/(3*x) + + (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, x])/(3*x) + (896*(1 + x)^3*H[0, 1, -1, x])/(9*x) - (256*(1 + x)^3*H[0, 1, 1, x])/ - (9*x)) + H[1, x]*((8*(1080 - 557*x - 4313*x^2 + 34345*x^3 - + (9*x)) + H[1, x]*((8*(1080 - 557*x - 4313*x^2 + 34345*x^3 - 137403*x^4 + 231804*x^5 - 170532*x^6 + 45360*x^7))/ - (81*(-1 + x)*x) - (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - - (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + - (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[0, -1, x])/(3*x^2) - + (81*(-1 + x)*x) - (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + (2048*(-21 + 19*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + (16*(-1 + x)*(-20 + 25*x - 53*x^2 + 18*x^3)*H[0, -1, x])/(3*x^2) - (16*(-20 + 35*x - 182*x^2 + 362*x^3 - 203*x^4 + 12*x^5)*H[0, 1, x])/ - (3*(-1 + x)*x^2) + (3584*(-1 + x)*H[0, 0, -1, x])/3 + - (16*(-52 + 465*x - 405*x^2 + 16*x^3)*H[0, 0, 1, x])/(9*x) - - (16*(12 - 131*x + 111*x^2)*H[0, 1, 1, x])/(3*x)) + - (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, -1, x])/(9*x) - - (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + - (32*(-28 - 291*x + 255*x^2 + 10*x^3)*H[0, -1, 0, 1, x])/(9*x) - - (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + - (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + - (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, -1, x])/(3*x) - - (64*(11 + 30*x + 5*x^3)*H[0, 0, -1, 1, x])/(3*x) + - (32*(58 - 192*x + 501*x^2 + 70*x^3)*H[0, 0, 0, -1, x])/(9*x) - - (64*(-11 + 452*x + 560*x^2 + 27*x^3)*H[0, 0, 0, 1, x])/(9*x) - - (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, -1, x])/(3*x) + - (16*(-52 - 38*x + 199*x^2 + 44*x^3)*H[0, 0, 1, 1, x])/(9*x) - - (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + - (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + - (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) - - (16*(-132 + 641*x - 451*x^2 + 24*x^3)*H[0, 1, 1, 1, x])/(9*x) + - H[0, x]*((8*(3240 + 67018*x + 211920*x^2 - 190999*x^3 - 412209*x^4 + - 695412*x^5 - 511596*x^6 + 136080*x^7))/(243*(-1 + x)*x) - + (3*(-1 + x)*x^2) + (3584*(-1 + x)*H[0, 0, -1, x])/3 + + (16*(-52 + 465*x - 405*x^2 + 16*x^3)*H[0, 0, 1, x])/(9*x) - + (16*(12 - 131*x + 111*x^2)*H[0, 1, 1, x])/(3*x)) + + (64*(1 + x)*(4 + 41*x + 4*x^2)*H[0, -1, -1, -1, x])/(9*x) - + (896*(1 + x)^3*H[0, -1, -1, 1, x])/(9*x) + + (32*(-28 - 291*x + 255*x^2 + 10*x^3)*H[0, -1, 0, 1, x])/(9*x) - + (896*(1 + x)^3*H[0, -1, 1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, -1, 1, 1, x])/(9*x) + + (32*(1 + x)*(1 + 2*x)*(22 + 5*x)*H[0, 0, -1, -1, x])/(3*x) - + (64*(11 + 30*x + 5*x^3)*H[0, 0, -1, 1, x])/(3*x) + + (32*(58 - 192*x + 501*x^2 + 70*x^3)*H[0, 0, 0, -1, x])/(9*x) - + (64*(-11 + 452*x + 560*x^2 + 27*x^3)*H[0, 0, 0, 1, x])/(9*x) - + (64*(1 + x)*(11 + 19*x + 5*x^2)*H[0, 0, 1, -1, x])/(3*x) + + (16*(-52 - 38*x + 199*x^2 + 44*x^3)*H[0, 0, 1, 1, x])/(9*x) - + (896*(1 + x)^3*H[0, 1, -1, -1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, -1, 1, x])/(9*x) + + (256*(1 + x)^3*H[0, 1, 1, -1, x])/(9*x) - + (16*(-132 + 641*x - 451*x^2 + 24*x^3)*H[0, 1, 1, 1, x])/(9*x) + + H[0, x]*((8*(3240 + 67018*x + 211920*x^2 - 190999*x^3 - 412209*x^4 + + 695412*x^5 - 511596*x^6 + 136080*x^7))/(243*(-1 + x)*x) - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x]^ - 2 - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, - x]*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - - 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 - - (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - - (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], - Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + - (8*(18 + 269*x - 311*x^2 + 18*x^3)*H[1, x]^2)/(9*x) - - (16*(-1 + x)*(2 + 7*x + 2*x^2)*H[1, x]^3)/(9*x) - - (32*(45 + 71*x^2)*H[-1, 1, x])/(3*x) + (32*(-1 + x)*H[0, -1, x]^2)/3 + + 2 - 8192*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, + x]*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x] - + 4096*(1 + x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x]^2 - + (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], (1 - VarGL)^(-1)}, x])/3 - + (2048*(-32 + 13*x)*GL[{Sqrt[1 - VarGL]*Sqrt[VarGL], + Sqrt[1 - VarGL]*Sqrt[VarGL], VarGL^(-1)}, x])/3 + + (8*(18 + 269*x - 311*x^2 + 18*x^3)*H[1, x]^2)/(9*x) - + (16*(-1 + x)*(2 + 7*x + 2*x^2)*H[1, x]^3)/(9*x) - + (32*(45 + 71*x^2)*H[-1, 1, x])/(3*x) + (32*(-1 + x)*H[0, -1, x]^2)/3 + (8*(180 - 963*x - 7894*x^2 + 7725*x^3 + 556*x^4 + 324*x^5)*H[0, 1, x])/ - (27*(-1 + x)*x^2) - (560*(1 + x)*H[0, 1, x]^2)/3 + + (27*(-1 + x)*x^2) - (560*(1 + x)*H[0, 1, x]^2)/3 + H[0, -1, x]*((8*(540 + 781*x + 1155*x^2 + 1866*x^3 + 108*x^4))/ - (27*x^2) + (832*(1 + x)*H[0, 1, x])/3) + - H[1, x]*((-8*(-54 - 10417*x + 10480*x^2 + 27*x^3))/(27*x) - + (27*x^2) + (832*(1 + x)*H[0, 1, x])/3) + + H[1, x]*((-8*(-54 - 10417*x + 10480*x^2 + 27*x^3))/(27*x) - (1792*(-1 + x)*H[0, -1, x])/3 + (16*(-52 - 333*x + 357*x^2 + 16*x^3)* H[0, 1, x])/(9*x)) - (64*(41 + 102*x - 39*x^2 + 15*x^3)* H[0, -1, -1, x])/(9*x) + (32*(22 - 165*x + 171*x^2 + 4*x^3)* @@ -1402,22 +1402,22 @@ H[0, 0, -1, x])/(3*x) + (16*(-44 + 776*x + 1349*x^2 + 48*x^3)* H[0, 0, 1, x])/(9*x) + (32*(22 - 165*x + 243*x^2 + 4*x^3)* H[0, 1, -1, x])/(9*x) - (16*(-52 - 713*x + 523*x^2 + 28*x^3)* - H[0, 1, 1, x])/(9*x) + (512*(-1 + x)*H[0, -1, -1, -1, x])/3 - + H[0, 1, 1, x])/(9*x) + (512*(-1 + x)*H[0, -1, -1, -1, x])/3 - (832*(1 + x)*H[0, -1, 0, 1, x])/3 - (896*(-1 + x)*H[0, 0, -1, -1, x])/ - 3 - (128*(19 + 13*x)*H[0, 0, -1, 1, x])/3 - - (32*(-195 + 43*x)*H[0, 0, 0, -1, x])/3 - - (32*(79 + 133*x)*H[0, 0, 0, 1, x])/3 - - (128*(19 + 13*x)*H[0, 0, 1, -1, x])/3 + - (1280*(1 + x)*H[0, 0, 1, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, 1, x])/3) + - (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + - (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + - (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + - (256*(8 + 5*x)*H[0, 0, -1, 0, 1, x])/3 + + 3 - (128*(19 + 13*x)*H[0, 0, -1, 1, x])/3 - + (32*(-195 + 43*x)*H[0, 0, 0, -1, x])/3 - + (32*(79 + 133*x)*H[0, 0, 0, 1, x])/3 - + (128*(19 + 13*x)*H[0, 0, 1, -1, x])/3 + + (1280*(1 + x)*H[0, 0, 1, 1, x])/3 + (64*(1 + x)*H[0, 1, 1, 1, x])/3) + + (1024*(-1 + x)*H[0, -1, 0, -1, -1, x])/3 + + (2048*(-1 + x)*H[0, 0, -1, -1, -1, x])/3 + + (640*(-1 + x)*H[0, 0, -1, 0, -1, x])/3 + + (256*(8 + 5*x)*H[0, 0, -1, 0, 1, x])/3 + 640*(-1 + x)*H[0, 0, 0, -1, -1, x] + 128*(19 + 13*x)* - H[0, 0, 0, -1, 1, x] - (256*(46 + 3*x)*H[0, 0, 0, 0, -1, x])/3 + + H[0, 0, 0, -1, 1, x] - (256*(46 + 3*x)*H[0, 0, 0, 0, -1, x])/3 + 128*(9 + 22*x)*H[0, 0, 0, 0, 1, x] + 128*(19 + 13*x)* - H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + - (128*(19 + 13*x)*H[0, 0, 1, 0, -1, x])/3 - + H[0, 0, 0, 1, -1, x] - 2208*(1 + x)*H[0, 0, 0, 1, 1, x] + + (128*(19 + 13*x)*H[0, 0, 1, 0, -1, x])/3 - (2464*(1 + x)*H[0, 0, 1, 0, 1, x])/3 + 1120*(1 + x)* - H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - + H[0, 0, 1, 1, 1, x] + (1568*(1 + x)*H[0, 1, 0, 1, 1, x])/3 - (32*(1 + x)*H[0, 1, 1, 1, 1, x])/3)); From 20e5703b8bd4bfc22d661d03edf1d0ee641a6276 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 13:52:47 +0100 Subject: [PATCH 06/18] fix minus sign and larger grid --- extras/ome_n3lo/convert_ome_xspace.py | 2 +- extras/ome_n3lo/large_n_limit.py | 2 +- .../notebooks/Agg_Aqq_largeN_expansion.nb | 167 +++++++++++------- 3 files changed, 101 insertions(+), 70 deletions(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 68f807c9b..6e97717dd 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -11,7 +11,7 @@ from large_n_limit import Agg_asymptotic, Aqq_asymptotic -XGRID = np.geomspace(1e-6, 1, 100) # 500 +XGRID = np.geomspace(1e-6, 1, 500) """X-grid.""" LOG = 0 diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index d398df5f7..c9daf1097 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -31,7 +31,7 @@ def Agg_asymptotic(n, nf): + 28.65462637880661 * nf ) agg_asy = ( - 49.5041510989361 * (-14.442649813264895 + nf) * S1(n) + - 49.5041510989361 * (-14.442649813264895 + nf) * S1(n) + 619.2420126046355 - 17.52475977636971 * nf ) diff --git a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb index 10f64212b..c7432a519 100644 --- a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb +++ b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb @@ -1,7 +1,5 @@ (* Content-type: application/vnd.wolfram.mathematica *) - - (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) @@ -12,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 44215, 1218] -NotebookOptionsPosition[ 40619, 1155] -NotebookOutlinePosition[ 41011, 1171] -CellTagsIndexPosition[ 40968, 1168] +NotebookDataLength[ 45418, 1251] +NotebookOptionsPosition[ 41686, 1185] +NotebookOutlinePosition[ 42083, 1201] +CellTagsIndexPosition[ 42040, 1198] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -595,16 +593,12 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox[ - RowBox[{ - StyleBox[ - RowBox[{"(", "*"}]], " ", + RowBox[{"(*", " ", RowBox[{ RowBox[{"Gluon", " ", "Limit"}], ",", " ", RowBox[{ "aggQ3", " ", "expansion", " ", "is", " ", "added", " ", "later"}]}], - " ", - StyleBox[ - RowBox[{"*", ")"}]]}], "Code"], + " ", "*)"}], "Code"], StyleBox["\n", "Code"], RowBox[{ RowBox[{ @@ -922,9 +916,9 @@ Cell[BoxData[ 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, 3.9489508160515337`*^9}, {3.948950869142365*^9, 3.948950905994871*^9}, { 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, - 3.9489536787425423`*^9}}, + 3.9489536787425423`*^9}, {3.948958133019916*^9, 3.948958153225314*^9}}, CellLabel-> - "In[271]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], + "In[304]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], Cell[BoxData[ RowBox[{"{", @@ -966,11 +960,14 @@ Cell[BoxData[ CellChangeTimes->{{3.948950056566019*^9, 3.9489500690040627`*^9}, 3.948950232810248*^9, {3.948950736657477*^9, 3.948950820817873*^9}, { 3.9489508804035892`*^9, 3.948950910733629*^9}, {3.948951248372204*^9, - 3.9489512628739233`*^9}, 3.948953684019939*^9}, + 3.9489512628739233`*^9}, 3.948953684019939*^9, {3.94895813931703*^9, + 3.94895815790287*^9}}, CellLabel-> - "Out[271]=",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] + "Out[304]=",ExpressionUUID->"5ca5ecef-8727-4600-b29d-d7a1547e3854"] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ RowBox[{"(*", @@ -994,7 +991,8 @@ Cell[BoxData[ RowBox[{ RowBox[{"1", "/", RowBox[{"(", - RowBox[{"1", "-", "x"}], ")"}]}], + RowBox[{ + RowBox[{"-", "1"}], "+", "x"}], ")"}]}], RowBox[{"(", RowBox[{ RowBox[{"x", "^", @@ -1004,8 +1002,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", ",", "0"}], "]"}]}], " ", "\[Equal]", " ", - RowBox[{"-", " ", - RowBox[{"LG", "[", "N", "]"}]}]}], ",", " ", + RowBox[{"LG", "[", "N", "]"}]}], ",", " ", RowBox[{ RowBox[{ "so", " ", "we", " ", "add", " ", "the", " ", "piece", " ", "with", " ", @@ -1015,7 +1012,7 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ggasy", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", "-", " ", + RowBox[{"[", "1", "]"}], "]"}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"aggQ3PLU", " ", "/.", " ", @@ -1035,11 +1032,10 @@ Cell[BoxData[ " ", "//", " ", "Simplify"}]}]}]], "Code", CellChangeTimes->{{3.948951282360952*^9, 3.948951363262577*^9}, { 3.9489533926644917`*^9, 3.9489534137431717`*^9}, {3.94895350090244*^9, - 3.948953641550552*^9}}, + 3.948953641550552*^9}, {3.948958049999295*^9, 3.948958079919736*^9}, { + 3.9489581700994253`*^9, 3.948958183399843*^9}}, CellLabel-> - "In[274]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], - -Cell[CellGroupData[{ + "In[308]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], Cell[BoxData[ RowBox[{"{", @@ -1051,37 +1047,32 @@ Cell[BoxData[ RowBox[{"LG", "[", "N", "]"}]}], ",", RowBox[{ RowBox[{"-", "72.36717694258661`"}], "+", - RowBox[{"3.11448410587291`", " ", "NF"}]}]}]}]], "Input", - CellChangeTimes->{{3.94895526412346*^9, - 3.9489552641239967`*^9}},ExpressionUUID->"5fe5ca95-25a2-4b98-8659-\ -62b0932393c1"], + RowBox[{"3.11448410587291`", " ", "NF"}]}]}], "}"}]], "Output", + CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, + 3.948958183986207*^9}, + CellLabel-> + "Out[308]=",ExpressionUUID->"345dea13-c1cd-46d2-a3fe-00f7e8568f58"], Cell[BoxData[ RowBox[{ RowBox[{"(", - RowBox[{ - RowBox[{"-", "1384.1265693540154`"}], "+", - RowBox[{"91.34702095227367`", " ", "NF"}]}], ")"}], " ", + RowBox[{"45.81566789575811`", "\[VeryThinSpace]", "-", + RowBox[{"7.661281245598531`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { - 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881680107`*^9}, + CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, + 3.948958183987544*^9}, CellLabel-> - "Out[275]=",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], + "Out[309]=",ExpressionUUID->"e436d0bd-f7c1-4e66-9fd4-a393fd05a59c"], Cell[BoxData[ RowBox[{"53.795479857509356`", "\[VeryThinSpace]", "+", RowBox[{"11.129866602436904`", " ", "NF"}]}]], "Output", - CellChangeTimes->{{3.9489512846997757`*^9, 3.948951364170044*^9}, { - 3.9489536257938213`*^9, 3.948953643832828*^9}, 3.9489536881693697`*^9}, + CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, + 3.948958183988996*^9}, CellLabel-> - "Out[276]=",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] + "Out[310]=",ExpressionUUID->"0c6394c7-120c-47f8-8b56-c35d5068eb44"] }, Open ]], -Cell[BoxData[""], "Input", - CellChangeTimes->{{3.94895127781951*^9, - 3.9489512801199293`*^9}},ExpressionUUID->"783fabf2-705a-4b70-bf99-\ -6b0e4f5b0b1c"], - Cell[CellGroupData[{ Cell[BoxData[{ @@ -1093,7 +1084,7 @@ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"-", " ", + RowBox[{"+", " ", RowBox[{"(", RowBox[{"aggQ3PLU", " ", "/.", " ", RowBox[{"z4", " ", "->", " ", @@ -1113,9 +1104,10 @@ Cell[BoxData[{ RowBox[{"z4", " ", "->", " ", RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], " ", "//", " ", "Simplify"}]}], "Input", - CellChangeTimes->{{3.948955379166621*^9, 3.948955399860025*^9}}, + CellChangeTimes->{{3.948955379166621*^9, 3.948955399860025*^9}, { + 3.948958194911723*^9, 3.948958195199505*^9}}, CellLabel-> - "In[282]:=",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], + "In[311]:=",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], Cell[BoxData[ RowBox[{ @@ -1124,39 +1116,75 @@ Cell[BoxData[ RowBox[{"-", "669.1554507291286`"}], "+", RowBox[{"41.84286985333757`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{3.948955511242378*^9}, + CellChangeTimes->{3.948955511242378*^9, 3.948958195859767*^9}, CellLabel-> - "Out[282]=",ExpressionUUID->"fecf1ce3-f280-4ff0-aaf4-d1f070df2ddf"], + "Out[311]=",ExpressionUUID->"b988ffc4-7572-471d-8239-4575847456a9"], Cell[BoxData[ - RowBox[{"49.5041510989361`", " ", + RowBox[{ + RowBox[{"-", "49.5041510989361`"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14.442649813264895`"}], "+", RowBox[{"1.`", " ", "NF"}]}], ")"}], " ", RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{3.948955511245875*^9}, + CellChangeTimes->{3.948955511242378*^9, 3.948958195861207*^9}, CellLabel-> - "Out[283]=",ExpressionUUID->"9fa3cc0f-c485-4e1b-b7d3-c134806ba903"], + "Out[312]=",ExpressionUUID->"b8ee1179-8690-4170-978a-4aecd92c574b"], Cell[BoxData[ RowBox[{ RowBox[{"-", "565.4465327471261`"}], "+", RowBox[{"28.65462637880661`", " ", "NF"}]}]], "Output", - CellChangeTimes->{3.948955511247541*^9}, + CellChangeTimes->{3.948955511242378*^9, 3.948958195862665*^9}, CellLabel-> - "Out[284]=",ExpressionUUID->"667a9454-d21c-48cb-a4b6-9925a27a04ae"], + "Out[313]=",ExpressionUUID->"d63dc666-7e44-4d21-8d14-3e05799543fb"], Cell[BoxData[ RowBox[{"619.2420126046355`", "\[VeryThinSpace]", "-", RowBox[{"17.52475977636971`", " ", "NF"}]}]], "Output", - CellChangeTimes->{3.9489555112496243`*^9}, + CellChangeTimes->{3.948955511242378*^9, 3.948958195864217*^9}, + CellLabel-> + "Out[314]=",ExpressionUUID->"4fd282bd-3b9a-4ce5-8aa3-65d8486e87f6"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SExpansion", "[", " ", + RowBox[{ + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + RowBox[{"1", "/", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], "+", "x"}], ")"}]}], + RowBox[{"(", + RowBox[{ + RowBox[{"x", "^", + RowBox[{"(", + RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", " ", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", ",", + "0"}], "]"}]], "Input", + CellChangeTimes->{{3.948958104007937*^9, 3.94895810617143*^9}}, + CellLabel-> + "In[298]:=",ExpressionUUID->"f8a04396-35d6-45a1-a0d2-fb838e0523ce"], + +Cell[BoxData[ + TemplateBox[{ + RowBox[{"LG", "[", "n", "]"}], + RowBox[{ + RowBox[{"Re", "[", "n", "]"}], ">", "0"}]}, + "ConditionalExpression"]], "Output", + CellChangeTimes->{3.948958109768873*^9}, CellLabel-> - "Out[285]=",ExpressionUUID->"c19edfde-8d03-4857-97d7-b87ff1d81deb"] + "Out[298]=",ExpressionUUID->"e3f4f8e2-7714-41c4-8b77-12ebd7cbf2ef"] }, Open ]] }, -WindowSize->{1920, 964}, -WindowMargins->{{0, Automatic}, {Automatic, 0}}, +WindowSize->{1792, 1067}, +WindowMargins->{{-1792, Automatic}, {Automatic, 0}}, FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) (June 19, 2020)", StyleDefinitions->"Default.nb", ExpressionUUID->"0a91d6a6-431d-4145-bf7f-17f592570909" @@ -1205,22 +1233,25 @@ Cell[17783, 524, 2053, 55, 97, "Output",ExpressionUUID->"31a2b1bc-7efa-42df-bd24 Cell[19839, 581, 300, 6, 34, "Output",ExpressionUUID->"c46fc0e1-a4fd-40d6-8949-8d1c6b684e2a"] }, Open ]], Cell[CellGroupData[{ -Cell[20176, 592, 12837, 332, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], -Cell[33016, 926, 1469, 42, 51, "Output",ExpressionUUID->"c1f0dc65-248b-4cf8-9116-06006ef31945"] +Cell[20176, 592, 12813, 328, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], +Cell[32992, 922, 1517, 43, 51, "Output",ExpressionUUID->"5ca5ecef-8727-4600-b29d-d7a1547e3854"] +}, Open ]], +Cell[CellGroupData[{ +Cell[34546, 970, 2450, 67, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], +Cell[36999, 1039, 542, 14, 34, "Output",ExpressionUUID->"345dea13-c1cd-46d2-a3fe-00f7e8568f58"], +Cell[37544, 1055, 383, 9, 34, "Output",ExpressionUUID->"e436d0bd-f7c1-4e66-9fd4-a393fd05a59c"], +Cell[37930, 1066, 307, 6, 34, "Output",ExpressionUUID->"0c6394c7-120c-47f8-8b56-c35d5068eb44"] }, Open ]], -Cell[34500, 971, 2350, 66, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], Cell[CellGroupData[{ -Cell[36875, 1041, 486, 13, 30, "Input",ExpressionUUID->"5fe5ca95-25a2-4b98-8659-62b0932393c1"], -Cell[37364, 1056, 434, 10, 34, "Output",ExpressionUUID->"d8d631b4-23b8-415f-ab20-70370d6db87c"], -Cell[37801, 1068, 357, 6, 34, "Output",ExpressionUUID->"f30aef44-09bc-4ffd-9d52-2d1eb2107809"] +Cell[38274, 1077, 1109, 32, 94, "Input",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], +Cell[39386, 1111, 353, 9, 34, "Output",ExpressionUUID->"b988ffc4-7572-471d-8239-4575847456a9"], +Cell[39742, 1122, 383, 10, 34, "Output",ExpressionUUID->"b8ee1179-8690-4170-978a-4aecd92c574b"], +Cell[40128, 1134, 273, 6, 57, "Output",ExpressionUUID->"d63dc666-7e44-4d21-8d14-3e05799543fb"], +Cell[40404, 1142, 275, 5, 34, "Output",ExpressionUUID->"4fd282bd-3b9a-4ce5-8aa3-65d8486e87f6"] }, Open ]], -Cell[38173, 1077, 153, 3, 30, "Input",ExpressionUUID->"783fabf2-705a-4b70-bf99-6b0e4f5b0b1c"], Cell[CellGroupData[{ -Cell[38351, 1084, 1060, 31, 94, "Input",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], -Cell[39414, 1117, 331, 9, 34, "Output",ExpressionUUID->"fecf1ce3-f280-4ff0-aaf4-d1f070df2ddf"], -Cell[39748, 1128, 343, 9, 34, "Output",ExpressionUUID->"9fa3cc0f-c485-4e1b-b7d3-c134806ba903"], -Cell[40094, 1139, 251, 6, 34, "Output",ExpressionUUID->"667a9454-d21c-48cb-a4b6-9925a27a04ae"], -Cell[40348, 1147, 255, 5, 34, "Output",ExpressionUUID->"c19edfde-8d03-4857-97d7-b87ff1d81deb"] +Cell[40716, 1152, 663, 20, 30, "Input",ExpressionUUID->"f8a04396-35d6-45a1-a0d2-fb838e0523ce"], +Cell[41382, 1174, 288, 8, 46, "Output",ExpressionUUID->"e3f4f8e2-7714-41c4-8b77-12ebd7cbf2ef"] }, Open ]] } ] From 274487fadc4bc38c74f6e2c00d4fc9e1cabc6c00 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 16:49:27 +0100 Subject: [PATCH 07/18] add a test to see the accuracy --- extras/ome_n3lo/convert_ome_xspace.py | 3 +- extras/ome_n3lo/test_interpolation.py | 68 +++++++++++++++++++++++++++ 2 files changed, 70 insertions(+), 1 deletion(-) create mode 100644 extras/ome_n3lo/test_interpolation.py diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 6e97717dd..41a390c24 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -7,11 +7,12 @@ from eko.mellin import Path from ekore.harmonics import cache as c from ekore.operator_matrix_elements.unpolarized.space_like import as3 +from eko.interpolation import lambertgrid from scipy import integrate from large_n_limit import Agg_asymptotic, Aqq_asymptotic -XGRID = np.geomspace(1e-6, 1, 500) +XGRID = lambertgrid(500, 1e-6) """X-grid.""" LOG = 0 diff --git a/extras/ome_n3lo/test_interpolation.py b/extras/ome_n3lo/test_interpolation.py new file mode 100644 index 000000000..228ed7116 --- /dev/null +++ b/extras/ome_n3lo/test_interpolation.py @@ -0,0 +1,68 @@ +"""Here we test that integrating the x-space expressions we are indeed reproducing eko.""" + +import numpy as np +from scipy.integrate import quad +from scipy.interpolate import CubicSpline + +from convert_ome_xspace import LOG, MAP_ENTRIES, compute_ome +from large_n_limit import Agg_asymptotic, Aqq_asymptotic + + +def ome_regular(entry, nf): + grid = np.loadtxt(f"x_space/A_{entry}.txt") + return CubicSpline(grid[:, 0], grid[:, nf - 2]) + + +def ome_local(entry, nf): + if entry == "gg": + return Agg_asymptotic(0, nf) + elif entry in ["qq_ns", "qq"]: + return Aqq_asymptotic(0, nf) + return 0 + + +def ome_singular(x, entry, nf): + local = ome_local(entry, nf) + if entry == "gg": + asy = Agg_asymptotic(1, nf) + elif entry in ["qq_ns", "qq"]: + asy = Aqq_asymptotic(1, nf) + + singular = np.real((asy - local)) + return singular / (- 1 + x) + + +def test_moments(entry, N, nf): + # compute N space ome form eko + is_singlet = "ns" not in entry + + ome_n = compute_ome(nf, complex(N), is_singlet) + idx1, idx2 = MAP_ENTRIES[entry] + ome_n = ome_n[idx1, idx2] + + # integrate using the x-space inteprolation + a_reg = ome_regular(entry, nf) + ome_x = quad(lambda x: a_reg(x) * x ** (N - 1), 1e-6, 1)[0] + + # add local and singular bits + if entry in ["qq_ns", "qq", "gg"]: + # pure plus term + ome_x += quad( + lambda x: ome_singular(x, entry, nf) * (x ** (N - 1) - 1), 1e-6, 1 + )[0] + # # constant part in N space, that should not be needed ? + # ome_x += quad( + # lambda x: - ome_singular(0, entry, nf) * x ** (N - 1), 1e-6, 1 + # )[0] + ome_x += ome_local(entry, nf) + + np.testing.assert_allclose(ome_n, ome_x, rtol=2e-2, err_msg=f"{entry}, {nf}") + + +if __name__ == "__main__": + N = 3.1233 + for nf in [3, 4, 5]: + # TODO: some entries are passing other no... + for k in ["qg"]: + # for k in ["gg", "qq", "qq_ns", "gq", "qg", "Hg", "Hq"]: + test_moments(k, N, nf) From e3101cb3e746ea94009225d2dbdae1957c15a4ff Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 18:32:51 +0100 Subject: [PATCH 08/18] fix qq limit and 5% accuracy, Hg not working --- extras/ome_n3lo/large_n_limit.py | 6 +++--- extras/ome_n3lo/test_interpolation.py | 24 ++++++++++++++---------- 2 files changed, 17 insertions(+), 13 deletions(-) diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index c9daf1097..71c237146 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -13,9 +13,9 @@ def Aqq_asymptotic(n, nf): """The N3LO quark-to-quark transition matrix element large-N limit.""" return ( - (20.36251906478134 - 3.4050138869326796 * nf) * S1(n) - - 72.36717694258661 - + 3.11448410587291 * nf + (20.362519064781296 - 3.4050138869326796 * nf) * S1(n) + - 51.033843609253296 + + 3.1144841058729096 * nf ) diff --git a/extras/ome_n3lo/test_interpolation.py b/extras/ome_n3lo/test_interpolation.py index 228ed7116..577dea1ae 100644 --- a/extras/ome_n3lo/test_interpolation.py +++ b/extras/ome_n3lo/test_interpolation.py @@ -1,6 +1,7 @@ """Here we test that integrating the x-space expressions we are indeed reproducing eko.""" import numpy as np +import pandas as pd from scipy.integrate import quad from scipy.interpolate import CubicSpline @@ -50,19 +51,22 @@ def test_moments(entry, N, nf): ome_x += quad( lambda x: ome_singular(x, entry, nf) * (x ** (N - 1) - 1), 1e-6, 1 )[0] - # # constant part in N space, that should not be needed ? - # ome_x += quad( - # lambda x: - ome_singular(0, entry, nf) * x ** (N - 1), 1e-6, 1 - # )[0] ome_x += ome_local(entry, nf) - np.testing.assert_allclose(ome_n, ome_x, rtol=2e-2, err_msg=f"{entry}, {nf}") + # TODO: some entries are passing other no... + # np.testing.assert_allclose(ome_n, ome_x, rtol=4e-2, err_msg=f"{entry}, {nf}") + return ome_n, ome_x if __name__ == "__main__": - N = 3.1233 + N = 4 + entries = ["gg", "qq", "qq_ns", "gq", "qg", "Hg", "Hq"] for nf in [3, 4, 5]: - # TODO: some entries are passing other no... - for k in ["qg"]: - # for k in ["gg", "qq", "qq_ns", "gq", "qg", "Hg", "Hq"]: - test_moments(k, N, nf) + results = [] + for k in entries: + results.append(test_moments(k, N, nf)) + df = pd.DataFrame(results, columns=["EKO", "Interpol"], index = entries, dtype=float) + df["rel_diff"] = ((df.EKO - df.Interpol) / df.EKO) + print("************************************") + print(df) + print("************************************") From c474d1e2163f39f5081ccb1cf4320331b508d3ef Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Wed, 19 Feb 2025 18:55:03 +0100 Subject: [PATCH 09/18] mathemetica notebook --- .../notebooks/Agg_Aqq_largeN_expansion.nb | 981 ++++++++++-------- 1 file changed, 572 insertions(+), 409 deletions(-) diff --git a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb index c7432a519..cbb77f886 100644 --- a/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb +++ b/extras/ome_n3lo/notebooks/Agg_Aqq_largeN_expansion.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 45418, 1251] -NotebookOptionsPosition[ 41686, 1185] -NotebookOutlinePosition[ 42083, 1201] -CellTagsIndexPosition[ 42040, 1198] +NotebookDataLength[ 50742, 1414] +NotebookOptionsPosition[ 47422, 1354] +NotebookOutlinePosition[ 47815, 1370] +CellTagsIndexPosition[ 47772, 1367] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -185,26 +185,14 @@ Cell[BoxData[ RowBox[{ RowBox[{"L", "[", "M", "]"}], "\[Rule]", " ", "Log"}]}], " ", "/.", " ", "QCDConst"}], " ", "//", " ", "ReduceToBasis"}], ",", " ", - "N", ",", " ", "order"}], "]"}]}], ";", "\n", "\t", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"expansion", ",", - RowBox[{"LG", "[", "N", "]"}]}], "]"}], - RowBox[{"LG", "[", "N", "]"}]}], ",", " ", - RowBox[{ - RowBox[{"expansion", " ", "-", - RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"expansion", ",", - RowBox[{"LG", "[", "N", "]"}]}], "]"}], - RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", "Simplify"}]}], - "}"}]}]}], "\n", "]"}]}]], "Code", + "N", ",", " ", "order"}], "]"}]}], ";", "\n", " ", "expansion"}]}], + "\n", "]"}]}]], "Code", CellChangeTimes->{{3.948948538528637*^9, 3.948948649446475*^9}, { - 3.948948844433375*^9, 3.948949008788335*^9}}, + 3.948948844433375*^9, 3.948949008788335*^9}, {3.948973544445546*^9, + 3.948973556977695*^9}, {3.948973614912841*^9, 3.948973627487043*^9}, { + 3.948973917143015*^9, 3.948973917434146*^9}}, CellLabel-> - "In[222]:=",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], + "In[408]:=",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], Cell[CellGroupData[{ @@ -226,18 +214,20 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", "\n", - RowBox[{"GetLargeXLimit", "[", - RowBox[{ + "1"}]}], ",", " ", "1", ",", "0"}], "]"}], "\n", "\n", + RowBox[{ + RowBox[{"GetLargeXLimit", "[", RowBox[{ - RowBox[{"Coefficient", "[", - RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", - " ", RowBox[{ + RowBox[{"Coefficient", "[", + RowBox[{"AqqQNS123N", ",", " ", "as", ",", "2"}], "]"}], " ", "/.", + " ", RowBox[{ - RowBox[{"(", - RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}], "\n", + RowBox[{ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", + RowBox[{"-", "1"}]}]}], ",", " ", "1", ",", "0"}], "]"}], " ", "//", + " ", "Expand"}], "\n", RowBox[{"Coefficient", "[", RowBox[{ RowBox[{ @@ -287,39 +277,41 @@ Cell[BoxData[ "}"}]}]}]}]], "Code", CellChangeTimes->{{3.948949013421583*^9, 3.9489490753518457`*^9}, { 3.948949822620695*^9, 3.948949849941022*^9}, {3.948950000521757*^9, - 3.948950014801219*^9}}, + 3.948950014801219*^9}, {3.94897363727754*^9, 3.948973643245582*^9}, { + 3.948974879541491*^9, 3.948974883828026*^9}}, CellLabel-> - "In[223]:=",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], + "In[442]:=",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], -Cell[BoxData[ - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}]], "Output", +Cell[BoxData["0"], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, - 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9}, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9, { + 3.948973630830533*^9, 3.948973644211673*^9}, 3.948973770938191*^9, + 3.9489739236565437`*^9, 3.948974884901483*^9}, CellLabel-> - "Out[223]=",ExpressionUUID->"932538e5-3fcc-4d6a-8839-992b3e2af928"], + "Out[442]=",ExpressionUUID->"73c1c6bb-5b3d-48b1-abae-caba061e3052"], Cell[BoxData[ - RowBox[{"{", - RowBox[{ - RowBox[{"-", - FractionBox[ - RowBox[{"448", " ", - RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ",", - RowBox[{ - FractionBox["1", "27"], " ", - RowBox[{"(", - RowBox[{"73", "+", - RowBox[{"80", " ", "z2"}], "-", - RowBox[{"48", " ", "z3"}]}], ")"}]}]}], "}"}]], "Output", + RowBox[{ + FractionBox["73", "27"], "-", + FractionBox["464", + RowBox[{"81", " ", "N"}]], "+", + FractionBox[ + RowBox[{"80", " ", "z2"}], "27"], "-", + FractionBox[ + RowBox[{"16", " ", "z3"}], "9"], "-", + FractionBox[ + RowBox[{"448", " ", + RowBox[{"LG", "[", "N", "]"}]}], "81"]}]], "Output", CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, - 3.948950002023658*^9, 3.948951086434144*^9, 3.9489511458553877`*^9}, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9, { + 3.948973630830533*^9, 3.948973644211673*^9}, 3.948973770938191*^9, + 3.9489739236565437`*^9, 3.948974884975451*^9}, CellLabel-> - "Out[224]=",ExpressionUUID->"0ccc496d-ebd3-4707-91cd-5192d14850da"], + "Out[443]=",ExpressionUUID->"c846b7df-d58d-49e9-b3e2-064039dbb79d"], Cell[BoxData[ RowBox[{"-", @@ -327,16 +319,11 @@ Cell[BoxData[ CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, - 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145856818*^9}, - CellLabel-> - "Out[225]=",ExpressionUUID->"580512ef-0d2c-49df-9693-7668a37ccce8"], - -Cell[BoxData["\<\"Cannot load 'SExpTab2'. Proceed without precomputed \ -expansions.\"\>"], "Print", - CellChangeTimes->{3.948951086526724*^9, 3.948951145878625*^9}, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9, { + 3.948973630830533*^9, 3.948973644211673*^9}, 3.948973770938191*^9, + 3.9489739236565437`*^9, 3.9489748849768763`*^9}, CellLabel-> - "During evaluation of \ -In[223]:=",ExpressionUUID->"c498f812-14d3-4a68-9da2-c8e933e5afc4"], + "Out[444]=",ExpressionUUID->"5ddf7606-a43f-4f37-8aca-667f6e70feab"], Cell[BoxData[ RowBox[{ @@ -370,9 +357,11 @@ Cell[BoxData[ CellChangeTimes->{ 3.948948910103238*^9, {3.9489489497659807`*^9, 3.948948973639214*^9}, { 3.948949011267372*^9, 3.9489490566612997`*^9}, 3.948949832646501*^9, - 3.948950002023658*^9, 3.948951086434144*^9, 3.948951146118248*^9}, + 3.948950002023658*^9, 3.948951086434144*^9, 3.948951145783738*^9, { + 3.948973630830533*^9, 3.948973644211673*^9}, 3.948973770938191*^9, + 3.9489739236565437`*^9, 3.948974885054215*^9}, CellLabel-> - "Out[226]=",ExpressionUUID->"918f1b3f-684b-41b7-bb1e-09e8ac524de5"] + "Out[445]=",ExpressionUUID->"4655a273-3664-439b-8d38-2bd10c0e12c3"] }, Open ]], Cell[CellGroupData[{ @@ -400,13 +389,14 @@ Cell[BoxData[ ",", " ", "1"}], "]"}]}]], "Code", CellChangeTimes->{{3.948950247009811*^9, 3.948950270110826*^9}}, CellLabel-> - "In[227]:=",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], + "In[413]:=",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], Cell[BoxData["0"], "Output", CellChangeTimes->{3.948950271429709*^9, 3.9489510906139727`*^9, - 3.948951149651967*^9}, + 3.948951149651967*^9, 3.948973655713615*^9, 3.9489737737158403`*^9, + 3.9489739270199747`*^9}, CellLabel-> - "Out[227]=",ExpressionUUID->"d3bc2ff3-a6a1-4b6c-985e-9651a6d3b117"] + "Out[413]=",ExpressionUUID->"3e32d8f1-4255-4413-9578-c332423e34f0"] }, Open ]], Cell[CellGroupData[{ @@ -426,69 +416,151 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - RowBox[{"-", "1"}]}]}], ",", " ", "0", ",", "0"}], "]"}]}]}]], "Code", + RowBox[{"-", "1"}]}]}], ",", " ", "1", ",", " ", "0"}], + "]"}]}]}]], "Code", CellChangeTimes->{{3.948950027207466*^9, 3.948950027437483*^9}, { - 3.9489501048247967`*^9, 3.948950153621386*^9}, 3.948951106558529*^9}, + 3.9489501048247967`*^9, 3.948950153621386*^9}, 3.948951106558529*^9, + 3.9489679658262663`*^9, {3.9489734784444532`*^9, 3.948973478885206*^9}, { + 3.9489739635125513`*^9, 3.948973966656788*^9}}, + CellLabel-> + "In[415]:=",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], + +Cell[BoxData["\<\"Cannot load 'SExpTab2'. Proceed without precomputed \ +expansions.\"\>"], "Print", + CellChangeTimes->{3.94897396745498*^9}, CellLabel-> - "In[228]:=",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], + "During evaluation of \ +In[415]:=",ExpressionUUID->"06524227-cb92-4de4-b4e6-8f64f632ce29"], Cell[BoxData[ - RowBox[{"{", + RowBox[{ RowBox[{ - RowBox[{ + FractionBox["4", "729"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "9382"}], "+", + RowBox[{"1183", " ", "NF"}], "+", + RowBox[{"16686", " ", "z4"}]}], ")"}]}], "-", + FractionBox[ + RowBox[{"4", " ", RowBox[{"(", + RowBox[{"45331", "+", + RowBox[{"3296", " ", "NF"}], "+", + RowBox[{"33372", " ", "z4"}]}], ")"}]}], + RowBox[{"2187", " ", "N"}]], "-", + FractionBox[ + RowBox[{"1184", " ", "z5"}], "81"], "+", + RowBox[{ + SuperscriptBox["z2", "2"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["4096", "1215"]}], "-", + FractionBox["128", + RowBox[{"15", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", "NF"}], "405"], "-", + FractionBox[ + RowBox[{"256", " ", + RowBox[{"LG", "[", "N", "]"}]}], "15"]}], ")"}]}], "+", + RowBox[{ + SuperscriptBox["ln2", "2"], " ", "z2", " ", + RowBox[{"(", + RowBox[{ + FractionBox["64", "9"], "-", + FractionBox["128", + RowBox[{"27", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", + RowBox[{"LG", "[", "N", "]"}]}], "27"]}], ")"}]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["85280", + RowBox[{"729", " ", "N"}]]}], "-", + FractionBox[ + RowBox[{"8", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "17705"}], "+", + RowBox[{"3008", " ", "NF"}], "+", + RowBox[{"33372", " ", "z4"}]}], ")"}]}], "2187"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], "+", + FractionBox[ + RowBox[{"368", " ", + SuperscriptBox[ + RowBox[{"LG", "[", "N", "]"}], "2"]}], + RowBox[{"81", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox[ + RowBox[{"LG", "[", "N", "]"}], "3"]}], + RowBox[{"243", " ", "N"}]], "+", + RowBox[{ + SuperscriptBox["ln2", "4"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["32", "27"]}], "+", + FractionBox["64", + RowBox[{"81", " ", "N"}]], "+", + FractionBox[ + RowBox[{"128", " ", + RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ")"}]}], "+", + RowBox[{"li4half", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["256", "9"]}], "+", + FractionBox["512", + RowBox[{"27", " ", "N"}]], "+", + FractionBox[ + RowBox[{"1024", " ", + RowBox[{"LG", "[", "N", "]"}]}], "27"]}], ")"}]}], "+", + RowBox[{"z2", " ", + RowBox[{"(", + RowBox[{ + FractionBox["1568", "243"], "+", + FractionBox["21920", + RowBox[{"243", " ", "N"}]], "+", + FractionBox[ + RowBox[{"128", " ", "NF"}], "243"], "+", + FractionBox[ + RowBox[{"4768", " ", "z3"}], "81"], "+", RowBox[{ - FractionBox["141640", "2187"], "+", - FractionBox[ - RowBox[{"1024", " ", "li4half"}], "27"], "+", - FractionBox[ - RowBox[{"128", " ", - SuperscriptBox["ln2", "4"]}], "81"], "-", - FractionBox[ - RowBox[{"24064", " ", "NF"}], "2187"], "+", - FractionBox[ - RowBox[{"6592", " ", "z2"}], "81"], "-", - FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", - FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["z2", "2"]}], "15"], "-", - FractionBox[ - RowBox[{"280", " ", "z3"}], "27"], "+", - FractionBox[ - RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", - FractionBox[ - RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{"-", + RowBox[{"(", + RowBox[{ + FractionBox["6592", "81"], "+", + FractionBox["2272", + RowBox[{"81", " ", "N"}]]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}], "+", + RowBox[{"z3", " ", + RowBox[{"(", RowBox[{ - FractionBox["1", "3645"], - RowBox[{"2", " ", + RowBox[{"-", + FractionBox["12938", "81"]}], "-", + FractionBox[ + RowBox[{"512", " ", "NF"}], "243"], "+", + FractionBox[ + RowBox[{ + FractionBox["12532", "243"], "+", + FractionBox[ + RowBox[{"256", " ", "NF"}], "81"]}], "N"], "+", + RowBox[{ RowBox[{"(", - RowBox[{"132700", "+", - RowBox[{"51840", " ", "li4half"}], "+", - RowBox[{"2160", " ", - SuperscriptBox["ln2", "4"]}], "-", - RowBox[{"11830", " ", "NF"}], "-", - RowBox[{"11760", " ", "z2"}], "-", - RowBox[{"12960", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "-", - RowBox[{"960", " ", "NF", " ", "z2"}], "+", - RowBox[{"6144", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"1152", " ", "NF", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"291105", " ", "z3"}], "+", - RowBox[{"3840", " ", "NF", " ", "z3"}], "-", - RowBox[{"107280", " ", "z2", " ", "z3"}], "-", - RowBox[{"166860", " ", "z4"}], "+", - RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", + RowBox[{ + RowBox[{"-", + FractionBox["280", "27"]}], "+", + FractionBox[ + RowBox[{"512", " ", "NF"}], "81"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}]}]], "Output", CellChangeTimes->{{3.9489500247139473`*^9, 3.948950039220125*^9}, 3.948950111791774*^9, 3.948950157878325*^9, 3.94895110422303*^9, - 3.948951163201816*^9}, + 3.948951163201816*^9, 3.9489734848278646`*^9, 3.948973669006665*^9, + 3.948973787035245*^9, 3.948973940261176*^9, 3.948973983118998*^9}, CellLabel-> - "Out[228]=",ExpressionUUID->"14f874a8-730a-4bee-bb0b-f93be4c938f2"] + "Out[415]=",ExpressionUUID->"b64d65c0-b205-41ed-89ab-174b040ce213"] }, Open ]], Cell[CellGroupData[{ @@ -511,81 +583,155 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + "1"}]}], ",", " ", "1", ",", " ", "0"}], "]"}]}], "\n", RowBox[{"(*", " ", RowBox[{ "check", " ", "that", " ", "the", " ", "2", " ", "are", " ", "the", " ", "same"}], " ", "*)"}], "\n", RowBox[{"qqNSasy", " ", "-", " ", "qqSasy"}]}]}]], "Code", CellChangeTimes->{{3.9489500926863003`*^9, 3.9489501123045464`*^9}, { - 3.948950162196804*^9, 3.948950206961136*^9}}, + 3.948950162196804*^9, 3.948950206961136*^9}, {3.9489734852331257`*^9, + 3.9489734866002493`*^9}, {3.948973976298914*^9, 3.9489739786025553`*^9}}, CellLabel-> - "In[231]:=",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], + "In[416]:=",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], Cell[BoxData[ - RowBox[{"{", + RowBox[{ RowBox[{ - RowBox[{ + FractionBox["4", "729"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "9382"}], "+", + RowBox[{"1183", " ", "NF"}], "+", + RowBox[{"16686", " ", "z4"}]}], ")"}]}], "-", + FractionBox[ + RowBox[{"4", " ", RowBox[{"(", + RowBox[{"45331", "+", + RowBox[{"3296", " ", "NF"}], "+", + RowBox[{"33372", " ", "z4"}]}], ")"}]}], + RowBox[{"2187", " ", "N"}]], "-", + FractionBox[ + RowBox[{"1184", " ", "z5"}], "81"], "+", + RowBox[{ + SuperscriptBox["z2", "2"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["4096", "1215"]}], "-", + FractionBox["128", + RowBox[{"15", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", "NF"}], "405"], "-", + FractionBox[ + RowBox[{"256", " ", + RowBox[{"LG", "[", "N", "]"}]}], "15"]}], ")"}]}], "+", + RowBox[{ + SuperscriptBox["ln2", "2"], " ", "z2", " ", + RowBox[{"(", + RowBox[{ + FractionBox["64", "9"], "-", + FractionBox["128", + RowBox[{"27", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", + RowBox[{"LG", "[", "N", "]"}]}], "27"]}], ")"}]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["85280", + RowBox[{"729", " ", "N"}]]}], "-", + FractionBox[ + RowBox[{"8", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "17705"}], "+", + RowBox[{"3008", " ", "NF"}], "+", + RowBox[{"33372", " ", "z4"}]}], ")"}]}], "2187"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], "+", + FractionBox[ + RowBox[{"368", " ", + SuperscriptBox[ + RowBox[{"LG", "[", "N", "]"}], "2"]}], + RowBox[{"81", " ", "N"}]], "-", + FractionBox[ + RowBox[{"256", " ", + SuperscriptBox[ + RowBox[{"LG", "[", "N", "]"}], "3"]}], + RowBox[{"243", " ", "N"}]], "+", + RowBox[{ + SuperscriptBox["ln2", "4"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["32", "27"]}], "+", + FractionBox["64", + RowBox[{"81", " ", "N"}]], "+", + FractionBox[ + RowBox[{"128", " ", + RowBox[{"LG", "[", "N", "]"}]}], "81"]}], ")"}]}], "+", + RowBox[{"li4half", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["256", "9"]}], "+", + FractionBox["512", + RowBox[{"27", " ", "N"}]], "+", + FractionBox[ + RowBox[{"1024", " ", + RowBox[{"LG", "[", "N", "]"}]}], "27"]}], ")"}]}], "+", + RowBox[{"z2", " ", + RowBox[{"(", + RowBox[{ + FractionBox["1568", "243"], "+", + FractionBox["21920", + RowBox[{"243", " ", "N"}]], "+", + FractionBox[ + RowBox[{"128", " ", "NF"}], "243"], "+", + FractionBox[ + RowBox[{"4768", " ", "z3"}], "81"], "+", RowBox[{ - FractionBox["141640", "2187"], "+", - FractionBox[ - RowBox[{"1024", " ", "li4half"}], "27"], "+", - FractionBox[ - RowBox[{"128", " ", - SuperscriptBox["ln2", "4"]}], "81"], "-", - FractionBox[ - RowBox[{"24064", " ", "NF"}], "2187"], "+", - FractionBox[ - RowBox[{"6592", " ", "z2"}], "81"], "-", - FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "27"], "-", - FractionBox[ - RowBox[{"256", " ", - SuperscriptBox["z2", "2"]}], "15"], "-", - FractionBox[ - RowBox[{"280", " ", "z3"}], "27"], "+", - FractionBox[ - RowBox[{"512", " ", "NF", " ", "z3"}], "81"], "-", - FractionBox[ - RowBox[{"3296", " ", "z4"}], "27"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{"-", + RowBox[{"(", + RowBox[{ + FractionBox["6592", "81"], "+", + FractionBox["2272", + RowBox[{"81", " ", "N"}]]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}], "+", + RowBox[{"z3", " ", + RowBox[{"(", RowBox[{ - FractionBox["1", "3645"], - RowBox[{"2", " ", + RowBox[{"-", + FractionBox["12938", "81"]}], "-", + FractionBox[ + RowBox[{"512", " ", "NF"}], "243"], "+", + FractionBox[ + RowBox[{ + FractionBox["12532", "243"], "+", + FractionBox[ + RowBox[{"256", " ", "NF"}], "81"]}], "N"], "+", + RowBox[{ RowBox[{"(", - RowBox[{"132700", "+", - RowBox[{"51840", " ", "li4half"}], "+", - RowBox[{"2160", " ", - SuperscriptBox["ln2", "4"]}], "-", - RowBox[{"11830", " ", "NF"}], "-", - RowBox[{"11760", " ", "z2"}], "-", - RowBox[{"12960", " ", - SuperscriptBox["ln2", "2"], " ", "z2"}], "-", - RowBox[{"960", " ", "NF", " ", "z2"}], "+", - RowBox[{"6144", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"1152", " ", "NF", " ", - SuperscriptBox["z2", "2"]}], "+", - RowBox[{"291105", " ", "z3"}], "+", - RowBox[{"3840", " ", "NF", " ", "z3"}], "-", - RowBox[{"107280", " ", "z2", " ", "z3"}], "-", - RowBox[{"166860", " ", "z4"}], "+", - RowBox[{"26640", " ", "z5"}]}], ")"}]}]}]}]}], "}"}]], "Output", + RowBox[{ + RowBox[{"-", + FractionBox["280", "27"]}], "+", + FractionBox[ + RowBox[{"512", " ", "NF"}], "81"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}]}]], "Output", CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { - 3.948950204161031*^9, 3.948950211058175*^9}, 3.948951193419348*^9}, + 3.948950204161031*^9, 3.948950211058175*^9}, 3.948951193419348*^9, { + 3.94897349234802*^9, 3.9489735008480873`*^9}, 3.948973681395398*^9, + 3.948973792558037*^9, 3.948973988394497*^9}, CellLabel-> - "Out[231]=",ExpressionUUID->"31a2b1bc-7efa-42df-bd24-d103791159cf"], + "Out[416]=",ExpressionUUID->"7e400a34-b1f8-4bae-8202-48168429017a"], -Cell[BoxData[ - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}]], "Output", +Cell[BoxData["0"], "Output", CellChangeTimes->{{3.9489500973100967`*^9, 3.9489501168546963`*^9}, { - 3.948950204161031*^9, 3.948950211058175*^9}, 3.9489511934214067`*^9}, + 3.948950204161031*^9, 3.948950211058175*^9}, 3.948951193419348*^9, { + 3.94897349234802*^9, 3.9489735008480873`*^9}, 3.948973681395398*^9, + 3.948973792558037*^9, 3.9489739883964357`*^9}, CellLabel-> - "Out[232]=",ExpressionUUID->"c46fc0e1-a4fd-40d6-8949-8d1c6b684e2a"] + "Out[417]=",ExpressionUUID->"1101aceb-7827-46cf-a76a-58e70dcaf0a3"] }, Open ]], Cell[CellGroupData[{ @@ -619,7 +765,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", " ", "N"}], " ", "\[Rule]", " ", - "1"}]}], ",", " ", "0", ",", "0"}], "]"}]}], "\n", + "1"}]}], ",", " ", "1", ",", " ", "0"}], "]"}]}], "\n", RowBox[{"(*", " ", RowBox[{ RowBox[{ @@ -911,59 +1057,109 @@ Cell[BoxData[ RowBox[{"-", "1"}]}], "]"}], " ", "/.", " ", "QCDConst"}]}], ";"}]}]}]], "Code", CellChangeTimes->{{3.948950055316721*^9, 3.948950063221066*^9}, { - 3.948950212826285*^9, 3.948950227872402*^9}, {3.948950356179121*^9, - 3.948950383652822*^9}, {3.948950501756506*^9, 3.948950536228887*^9}, { - 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, - 3.9489508160515337`*^9}, {3.948950869142365*^9, 3.948950905994871*^9}, { - 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, - 3.9489536787425423`*^9}, {3.948958133019916*^9, 3.948958153225314*^9}}, + 3.948950212826285*^9, 3.948950227872402*^9}, {3.948950356179121*^9, + 3.948950383652822*^9}, {3.948950501756506*^9, 3.948950536228887*^9}, { + 3.9489505670793133`*^9, 3.9489505676116056`*^9}, {3.94895063621457*^9, + 3.9489508160515337`*^9}, {3.948950869142365*^9, 3.948950905994871*^9}, { + 3.9489512071273737`*^9, 3.948951257781588*^9}, {3.948953658100237*^9, + 3.9489536787425423`*^9}, {3.948958133019916*^9, 3.948958153225314*^9}, { + 3.948973504254952*^9, 3.948973504433131*^9}, 3.948973761193138*^9, { + 3.948973992468505*^9, 3.948973997849969*^9}}, CellLabel-> - "In[304]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], + "In[436]:=",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], Cell[BoxData[ - RowBox[{"{", + RowBox[{ + RowBox[{"-", + FractionBox["12337", "27"]}], "+", + FractionBox[ + RowBox[{"58", " ", "NF"}], "3"], "+", + FractionBox[ + RowBox[{ + RowBox[{"-", + FractionBox["7490", "27"]}], "+", + FractionBox[ + RowBox[{"1528", " ", "NF"}], "81"]}], "N"], "-", + FractionBox[ + RowBox[{"128", " ", "ln2", " ", "z2"}], "9"], "+", + RowBox[{ + SuperscriptBox["z2", "2"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["12", "N"]}], "-", + RowBox[{"24", " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}], "+", RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["12820", "27"]}], "+", + FractionBox[ + RowBox[{ + FractionBox["416", "3"], "-", + FractionBox[ + RowBox[{"64", " ", "NF"}], "9"]}], "N"], "+", + FractionBox[ + RowBox[{"2624", " ", "NF"}], "81"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}], "+", + FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ - RowBox[{"-", - FractionBox["12820", "27"]}], "+", - FractionBox[ - RowBox[{"2624", " ", "NF"}], "81"], "-", - FractionBox[ - RowBox[{"556", " ", "z2"}], "9"], "+", + RowBox[{"-", "20"}], "+", FractionBox[ - RowBox[{"40", " ", "NF", " ", "z2"}], "9"], "-", - RowBox[{"24", " ", - SuperscriptBox["z2", "2"]}], "-", - FractionBox[ - RowBox[{"208", " ", "z3"}], "9"], "+", - FractionBox[ - RowBox[{"16", " ", "NF", " ", "z3"}], "9"]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{ - FractionBox["1", "27"], " ", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "12337"}], "+", - RowBox[{"9", " ", "NF", " ", - RowBox[{"(", - RowBox[{"58", "+", - RowBox[{"17", " ", "z2"}]}], ")"}]}], "+", - RowBox[{"88", " ", "z3"}], "-", - RowBox[{"3", " ", "z2", " ", + RowBox[{"4", " ", "NF"}], "3"]}], ")"}], " ", + SuperscriptBox[ + RowBox[{"LG", "[", "N", "]"}], "2"]}], "N"], "+", + RowBox[{"z3", " ", + RowBox[{"(", + RowBox[{ + FractionBox["88", "27"], "+", + FractionBox[ + RowBox[{"8", " ", RowBox[{"(", - RowBox[{"137", "+", - RowBox[{"128", " ", "ln2"}], "+", - RowBox[{"324", " ", "z3"}]}], ")"}]}]}], ")"}]}]}], "}"}]], "Output",\ - + RowBox[{ + RowBox[{"-", "13"}], "+", "NF"}], ")"}]}], + RowBox[{"9", " ", "N"}]], "+", + RowBox[{ + FractionBox["16", "9"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "13"}], "+", "NF"}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}], "+", + RowBox[{"z2", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["137", "9"]}], "+", + FractionBox[ + RowBox[{"17", " ", "NF"}], "3"], "+", + FractionBox[ + RowBox[{ + RowBox[{"-", + FractionBox["458", "9"]}], "+", + FractionBox[ + RowBox[{"32", " ", "NF"}], "9"]}], "N"], "-", + RowBox[{"36", " ", "z3"}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox["556", "9"]}], "+", + FractionBox["48", "N"], "+", + FractionBox[ + RowBox[{"40", " ", "NF"}], "9"]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}], ")"}]}]}]], "Output", CellChangeTimes->{{3.948950056566019*^9, 3.9489500690040627`*^9}, 3.948950232810248*^9, {3.948950736657477*^9, 3.948950820817873*^9}, { 3.9489508804035892`*^9, 3.948950910733629*^9}, {3.948951248372204*^9, 3.9489512628739233`*^9}, 3.948953684019939*^9, {3.94895813931703*^9, - 3.94895815790287*^9}}, + 3.94895815790287*^9}, 3.948973510426108*^9, 3.948973704365727*^9, + 3.948973766671776*^9, {3.948973797303988*^9, 3.948973820211097*^9}, + 3.948974003134963*^9, 3.948974701557065*^9}, CellLabel-> - "Out[304]=",ExpressionUUID->"5ca5ecef-8727-4600-b29d-d7a1547e3854"] + "Out[436]=",ExpressionUUID->"eb993488-92df-40bb-a9d6-ea6f151014e6"] }, Open ]], Cell[CellGroupData[{ @@ -975,216 +1171,189 @@ Cell[BoxData[ "\n", RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"qqNSasy", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", - " ", "Simplify"}], "\n", "\n", - RowBox[{"(*", " ", - RowBox[{ - RowBox[{ - RowBox[{"Here", " ", "we", " ", "have", " ", "that", " ", - RowBox[{"SExpansion", "[", " ", - RowBox[{ - RowBox[{"Integrate", "[", - RowBox[{ - RowBox[{ - RowBox[{"1", "/", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "1"}], "+", "x"}], ")"}]}], - RowBox[{"(", - RowBox[{ - RowBox[{"x", "^", - RowBox[{"(", - RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", - " ", - RowBox[{"{", - RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", - ",", "0"}], "]"}]}], " ", "\[Equal]", " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", " ", + RowBox[{"Series", "[", RowBox[{ RowBox[{ - "so", " ", "we", " ", "add", " ", "the", " ", "piece", " ", "with", " ", - "a"}], " ", "-", " ", - RowBox[{"sign", "!"}]}]}], " ", "*)"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"qqNSasy", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], " ", "//", " ", "Expand"}], ",", " ", + RowBox[{"{", + RowBox[{"N", ",", " ", "Infinity", ",", " ", "0"}], "}"}]}], "]"}], + " ", "//", " ", "Normal"}], "\n", "\n", RowBox[{ - RowBox[{ + RowBox[{"Series", "[", RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", "+", " ", RowBox[{ - RowBox[{"(", - RowBox[{"aggQ3PLU", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}], - RowBox[{"LG", "[", "N", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", - " ", "Simplify"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"ggasy", " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}], " ", "//", " ", "Expand"}], ",", " ", + RowBox[{"{", + RowBox[{"N", ",", " ", "Infinity", ",", " ", "0"}], "}"}]}], "]"}], + " ", "//", " ", "Normal"}], "\n", RowBox[{ RowBox[{ RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", "+", " ", - RowBox[{"(", - RowBox[{"aggQ3DEL", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], - " ", "//", " ", "Simplify"}]}]}]], "Code", + RowBox[{"aggQ3DEL", " ", "+", " ", + RowBox[{"aggQ3PLU", " ", + RowBox[{"LG", "[", "N", "]"}]}]}], " ", "/.", " ", + RowBox[{"z4", " ", "->", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], " ", "//", + " ", "Simplify"}]}]}]], "Code", CellChangeTimes->{{3.948951282360952*^9, 3.948951363262577*^9}, { 3.9489533926644917`*^9, 3.9489534137431717`*^9}, {3.94895350090244*^9, 3.948953641550552*^9}, {3.948958049999295*^9, 3.948958079919736*^9}, { - 3.9489581700994253`*^9, 3.948958183399843*^9}}, + 3.9489581700994253`*^9, 3.948958183399843*^9}, {3.9489738237090197`*^9, + 3.948973849702586*^9}, {3.94897401722054*^9, 3.948974090225195*^9}, { + 3.948974164679057*^9, 3.948974175115038*^9}}, CellLabel-> - "In[308]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], + "In[439]:=",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], Cell[BoxData[ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{"20.36251906478134`", "\[VeryThinSpace]", "-", - RowBox[{"3.4050138869326796`", " ", "NF"}]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}], ",", - RowBox[{ - RowBox[{"-", "72.36717694258661`"}], "+", - RowBox[{"3.11448410587291`", " ", "NF"}]}]}], "}"}]], "Output", - CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, - 3.948958183986207*^9}, + RowBox[{ + RowBox[{"-", "51.033843609253296`"}], "+", + RowBox[{"3.1144841058729096`", " ", "NF"}], "+", + RowBox[{"20.362519064781296`", " ", + RowBox[{"LG", "[", "N", "]"}]}], "-", + RowBox[{"3.4050138869326796`", " ", "NF", " ", + RowBox[{"LG", "[", "N", "]"}]}]}]], "Output", + CellChangeTimes->{3.948974705742137*^9}, CellLabel-> - "Out[308]=",ExpressionUUID->"345dea13-c1cd-46d2-a3fe-00f7e8568f58"], + "Out[439]=",ExpressionUUID->"cc271b25-2e33-4789-8505-58d7c6d45a79"], Cell[BoxData[ RowBox[{ - RowBox[{"(", - RowBox[{"45.81566789575811`", "\[VeryThinSpace]", "-", - RowBox[{"7.661281245598531`", " ", "NF"}]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, - 3.948958183987544*^9}, + RowBox[{"-", "565.4465327471261`"}], "+", + RowBox[{"28.65462637880661`", " ", "NF"}], "-", + RowBox[{"669.1554507291287`", " ", + RowBox[{"LG", "[", "N", "]"}]}], "+", + RowBox[{"41.84286985333757`", " ", "NF", " ", + RowBox[{"LG", "[", "N", "]"}]}]}]], "Output", + CellChangeTimes->{3.948974705743742*^9}, CellLabel-> - "Out[309]=",ExpressionUUID->"e436d0bd-f7c1-4e66-9fd4-a393fd05a59c"], + "Out[440]=",ExpressionUUID->"c2d7d4a3-ab23-4adf-9c7c-a1a08cc514ed"], Cell[BoxData[ - RowBox[{"53.795479857509356`", "\[VeryThinSpace]", "+", - RowBox[{"11.129866602436904`", " ", "NF"}]}]], "Output", - CellChangeTimes->{{3.948958053389802*^9, 3.9489580804770403`*^9}, - 3.948958183988996*^9}, + RowBox[{"619.2420126046354`", "\[VeryThinSpace]", "-", + RowBox[{"17.52475977636971`", " ", "NF"}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{"714.9711186248867`", "\[VeryThinSpace]", "-", + RowBox[{"49.5041510989361`", " ", "NF"}]}], ")"}], " ", + RowBox[{"LG", "[", "N", "]"}]}]}]], "Output", + CellChangeTimes->{3.948974705744967*^9}, CellLabel-> - "Out[310]=",ExpressionUUID->"0c6394c7-120c-47f8-8b56-c35d5068eb44"] + "Out[441]=",ExpressionUUID->"de2a2937-73e4-409a-bda3-dce529de38a9"] }, Open ]], Cell[CellGroupData[{ -Cell[BoxData[{ - RowBox[{ - RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\[IndentingNewLine]", +Cell[BoxData[ RowBox[{ + RowBox[{"(*", " ", + RowBox[{"X", "-", + RowBox[{"space", " ", "exspansion"}]}], " ", "*)"}], "\n", RowBox[{ RowBox[{ - RowBox[{"+", " ", - RowBox[{"(", - RowBox[{"aggQ3PLU", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], - RowBox[{"LG", "[", "N", "]"}]}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\n", - RowBox[{ - RowBox[{ - RowBox[{"ggasy", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", "//", " ", "N"}], " ", "//", " ", - "Simplify"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"+", " ", - RowBox[{"(", - RowBox[{"aggQ3DEL", " ", "/.", " ", - RowBox[{"z4", " ", "->", " ", - RowBox[{"Zeta", "[", "4", "]"}]}]}], ")"}]}], " ", "//", " ", "N"}], - " ", "//", " ", "Simplify"}]}], "Input", - CellChangeTimes->{{3.948955379166621*^9, 3.948955399860025*^9}, { - 3.948958194911723*^9, 3.948958195199505*^9}}, - CellLabel-> - "In[311]:=",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(", + RowBox[{ + RowBox[{"InvMellin", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"qqNSasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "+", " ", + RowBox[{"qqNSasy", "[", + RowBox[{"[", "2", "]"}], "]"}]}], " ", "/.", " ", + RowBox[{ + RowBox[{"LG", "[", "N", "]"}], " ", "\[Rule]", " ", + RowBox[{"S", "[", + RowBox[{"1", ",", " ", "N"}], "]"}]}]}], " ", "/.", " ", + RowBox[{"N", " ", "\[Rule]", " ", + RowBox[{"N", " ", "+", " ", "1"}]}]}], ",", " ", "N", ",", " ", + "x"}], "]"}], " ", "/.", " ", + RowBox[{"z4", " ", "\[Rule]", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}], "\n", RowBox[{ - RowBox[{"-", "669.1554507291286`"}], "+", - RowBox[{"41.84286985333757`", " ", "NF"}]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{3.948955511242378*^9, 3.948958195859767*^9}, - CellLabel-> - "Out[311]=",ExpressionUUID->"b988ffc4-7572-471d-8239-4575847456a9"], + RowBox[{ + RowBox[{"InvMellin", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"ggasy", "[", + RowBox[{"[", "1", "]"}], "]"}], " ", "+", " ", + RowBox[{"aggQ3PLU", " ", + RowBox[{"LG", "[", "N", "]"}]}], " ", "+", " ", + RowBox[{"ggasy", "[", + RowBox[{"[", "2", "]"}], "]"}], " ", "+", " ", "aggQ3DEL"}], " ", "/.", + " ", + RowBox[{ + RowBox[{"LG", "[", "N", "]"}], " ", "\[Rule]", " ", + RowBox[{"S", "[", + RowBox[{"1", ",", " ", "N"}], "]"}]}]}], " ", "/.", " ", + RowBox[{"N", " ", "\[Rule]", " ", + RowBox[{"N", " ", "+", " ", "1"}]}]}], ",", " ", "N", ",", " ", + "x"}], "]"}], " ", "/.", " ", + RowBox[{"z4", " ", "\[Rule]", " ", + RowBox[{"Zeta", "[", "4", "]"}]}]}], " ", "//", " ", "N"}]}]}]], "Code",\ -Cell[BoxData[ - RowBox[{ - RowBox[{"-", "49.5041510989361`"}], " ", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "14.442649813264895`"}], "+", - RowBox[{"1.`", " ", "NF"}]}], ")"}], " ", - RowBox[{"LG", "[", "N", "]"}]}]], "Output", - CellChangeTimes->{3.948955511242378*^9, 3.948958195861207*^9}, + CellChangeTimes->{{3.948962478557218*^9, 3.948962729528542*^9}, { + 3.9489629232696533`*^9, 3.9489629753338337`*^9}, {3.948967484061522*^9, + 3.948967516206167*^9}, 3.9489749300785713`*^9}, CellLabel-> - "Out[312]=",ExpressionUUID->"b8ee1179-8690-4170-978a-4aecd92c574b"], + "In[448]:=",ExpressionUUID->"af1435e5-10d6-484a-bbac-968a2283f2ae"], Cell[BoxData[ RowBox[{ - RowBox[{"-", "565.4465327471261`"}], "+", - RowBox[{"28.65462637880661`", " ", "NF"}]}]], "Output", - CellChangeTimes->{3.948955511242378*^9, 3.948958195862665*^9}, - CellLabel-> - "Out[313]=",ExpressionUUID->"d63dc666-7e44-4d21-8d14-3e05799543fb"], - -Cell[BoxData[ - RowBox[{"619.2420126046355`", "\[VeryThinSpace]", "-", - RowBox[{"17.52475977636971`", " ", "NF"}]}]], "Output", - CellChangeTimes->{3.948955511242378*^9, 3.948958195864217*^9}, - CellLabel-> - "Out[314]=",ExpressionUUID->"4fd282bd-3b9a-4ce5-8aa3-65d8486e87f6"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SExpansion", "[", " ", + RowBox[{"-", "148.97172557001937`"}], "-", + RowBox[{"6.028349336991313`", " ", "NF"}], "+", RowBox[{ - RowBox[{"Integrate", "[", - RowBox[{ - RowBox[{ - RowBox[{"1", "/", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "1"}], "+", "x"}], ")"}]}], - RowBox[{"(", - RowBox[{ - RowBox[{"x", "^", - RowBox[{"(", - RowBox[{"n", "-", "1"}], ")"}]}], "-", "1"}], ")"}]}], ",", " ", - RowBox[{"{", - RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "n", ",", - "0"}], "]"}]], "Input", - CellChangeTimes->{{3.948958104007937*^9, 3.94895810617143*^9}}, + RowBox[{"(", + RowBox[{"47.61396695585212`", "\[VeryThinSpace]", "+", + RowBox[{"6.491083676268861`", " ", "NF"}]}], ")"}], " ", + SubscriptBox["\[Delta]", + RowBox[{"1.`", "\[VeryThinSpace]", "-", + RowBox[{"1.`", " ", "x"}]}]]}]}]], "Output", + CellChangeTimes->{{3.948962527938343*^9, 3.94896254167848*^9}, + 3.948962615054599*^9, {3.9489626588074293`*^9, 3.94896267544433*^9}, { + 3.9489627153045588`*^9, 3.948962730273273*^9}, 3.948962977504568*^9, { + 3.948967508935272*^9, 3.948967519849976*^9}, 3.948974931742342*^9}, CellLabel-> - "In[298]:=",ExpressionUUID->"f8a04396-35d6-45a1-a0d2-fb838e0523ce"], + "Out[448]=",ExpressionUUID->"f193fda5-76ee-44fe-9d80-065cf5814180"], Cell[BoxData[ - TemplateBox[{ - RowBox[{"LG", "[", "n", "]"}], + RowBox[{"714.9711186248865`", "\[VeryThinSpace]", "-", + RowBox[{"49.50415109893609`", " ", "NF"}], "+", + FractionBox["714.9711186248865`", RowBox[{ - RowBox[{"Re", "[", "n", "]"}], ">", "0"}]}, - "ConditionalExpression"]], "Output", - CellChangeTimes->{3.948958109768873*^9}, + RowBox[{"-", "1.`"}], "+", "x"}]], "-", + FractionBox[ + RowBox[{"49.50415109893609`", " ", "NF"}], + RowBox[{ + RowBox[{"-", "1.`"}], "+", "x"}]], "+", + RowBox[{ + RowBox[{"(", + RowBox[{"162.31608667870944`", "\[VeryThinSpace]", "+", + RowBox[{"1.8085735569636259`", " ", "NF"}]}], ")"}], " ", + SubscriptBox["\[Delta]", + RowBox[{"1.`", "\[VeryThinSpace]", "-", + RowBox[{"1.`", " ", "x"}]}]]}]}]], "Output", + CellChangeTimes->{{3.948962527938343*^9, 3.94896254167848*^9}, + 3.948962615054599*^9, {3.9489626588074293`*^9, 3.94896267544433*^9}, { + 3.9489627153045588`*^9, 3.948962730273273*^9}, 3.948962977504568*^9, { + 3.948967508935272*^9, 3.948967519849976*^9}, 3.948974932101149*^9}, CellLabel-> - "Out[298]=",ExpressionUUID->"e3f4f8e2-7714-41c4-8b77-12ebd7cbf2ef"] + "Out[449]=",ExpressionUUID->"6b51c8f3-cf23-446f-b317-9ece5dd00c17"] }, Open ]] }, -WindowSize->{1792, 1067}, -WindowMargins->{{-1792, Automatic}, {Automatic, 0}}, +WindowSize->{1920, 1027}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) (June 19, 2020)", StyleDefinitions->"Default.nb", ExpressionUUID->"0a91d6a6-431d-4145-bf7f-17f592570909" @@ -1210,48 +1379,42 @@ Cell[2539, 80, 815, 22, 44, "Print",ExpressionUUID->"10592614-5c1d-48ee-b699-00d }, Open ]], Cell[3381, 106, 1784, 47, 148, "Code",ExpressionUUID->"3e9423b7-e0d4-4093-b3ce-955024eadbb5"], Cell[5168, 155, 485, 12, 94, "Input",ExpressionUUID->"38ac9fa3-fd03-4c80-97d5-f0a3587299c5"], -Cell[5656, 169, 1400, 37, 110, "Code",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], -Cell[CellGroupData[{ -Cell[7081, 210, 2840, 81, 148, "Code",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], -Cell[9924, 293, 393, 8, 34, "Output",ExpressionUUID->"932538e5-3fcc-4d6a-8839-992b3e2af928"], -Cell[10320, 303, 667, 18, 51, "Output",ExpressionUUID->"0ccc496d-ebd3-4707-91cd-5192d14850da"], -Cell[10990, 323, 389, 8, 51, "Output",ExpressionUUID->"580512ef-0d2c-49df-9693-7668a37ccce8"], -Cell[11382, 333, 269, 5, 24, "Print",ExpressionUUID->"c498f812-14d3-4a68-9da2-c8e933e5afc4"], -Cell[11654, 340, 1147, 34, 50, "Output",ExpressionUUID->"918f1b3f-684b-41b7-bb1e-09e8ac524de5"] -}, Open ]], +Cell[5656, 169, 1046, 25, 110, "Code",ExpressionUUID->"01d91176-3e08-4fab-b870-c3281dba1dc5"], Cell[CellGroupData[{ -Cell[12838, 379, 818, 23, 72, "Code",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], -Cell[13659, 404, 202, 4, 34, "Output",ExpressionUUID->"d3bc2ff3-a6a1-4b6c-985e-9651a6d3b117"] +Cell[6727, 198, 2990, 84, 148, "Code",ExpressionUUID->"9e895404-3e68-47b1-a1ba-9369dade9515"], +Cell[9720, 284, 470, 8, 34, "Output",ExpressionUUID->"73c1c6bb-5b3d-48b1-abae-caba061e3052"], +Cell[10193, 294, 767, 19, 51, "Output",ExpressionUUID->"c846b7df-d58d-49e9-b3e2-064039dbb79d"], +Cell[10963, 315, 513, 10, 51, "Output",ExpressionUUID->"5ddf7606-a43f-4f37-8aca-667f6e70feab"], +Cell[11479, 327, 1269, 36, 50, "Output",ExpressionUUID->"4655a273-3664-439b-8d38-2bd10c0e12c3"] }, Open ]], Cell[CellGroupData[{ -Cell[13898, 413, 749, 19, 72, "Code",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], -Cell[14650, 434, 2074, 56, 97, "Output",ExpressionUUID->"14f874a8-730a-4bee-bb0b-f93be4c938f2"] +Cell[12785, 368, 818, 23, 72, "Code",ExpressionUUID->"39f9f07e-6cb6-41bd-856a-3c5f12db5ad6"], +Cell[13606, 393, 275, 5, 34, "Output",ExpressionUUID->"3e32d8f1-4255-4413-9578-c332423e34f0"] }, Open ]], Cell[CellGroupData[{ -Cell[16761, 495, 1019, 27, 110, "Code",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], -Cell[17783, 524, 2053, 55, 97, "Output",ExpressionUUID->"31a2b1bc-7efa-42df-bd24-d103791159cf"], -Cell[19839, 581, 300, 6, 34, "Output",ExpressionUUID->"c46fc0e1-a4fd-40d6-8949-8d1c6b684e2a"] +Cell[13918, 403, 887, 22, 72, "Code",ExpressionUUID->"40ea46e3-0336-4631-b923-d508c835290c"], +Cell[14808, 427, 246, 5, 24, "Print",ExpressionUUID->"06524227-cb92-4de4-b4e6-8f64f632ce29"], +Cell[15057, 434, 3926, 128, 104, "Output",ExpressionUUID->"b64d65c0-b205-41ed-89ab-174b040ce213"] }, Open ]], Cell[CellGroupData[{ -Cell[20176, 592, 12813, 328, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], -Cell[32992, 922, 1517, 43, 51, "Output",ExpressionUUID->"5ca5ecef-8727-4600-b29d-d7a1547e3854"] +Cell[19020, 567, 1125, 28, 110, "Code",ExpressionUUID->"6a94d914-4abb-417f-9a1c-c6e6d734f02c"], +Cell[20148, 597, 3910, 128, 104, "Output",ExpressionUUID->"7e400a34-b1f8-4bae-8202-48168429017a"], +Cell[24061, 727, 376, 6, 34, "Output",ExpressionUUID->"1101aceb-7827-46cf-a76a-58e70dcaf0a3"] }, Open ]], Cell[CellGroupData[{ -Cell[34546, 970, 2450, 67, 148, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], -Cell[36999, 1039, 542, 14, 34, "Output",ExpressionUUID->"345dea13-c1cd-46d2-a3fe-00f7e8568f58"], -Cell[37544, 1055, 383, 9, 34, "Output",ExpressionUUID->"e436d0bd-f7c1-4e66-9fd4-a393fd05a59c"], -Cell[37930, 1066, 307, 6, 34, "Output",ExpressionUUID->"0c6394c7-120c-47f8-8b56-c35d5068eb44"] +Cell[24474, 738, 12946, 330, 452, "Code",ExpressionUUID->"fd46cc8c-2116-4631-9b82-3772d5dc4cba"], +Cell[37423, 1070, 2875, 91, 64, "Output",ExpressionUUID->"eb993488-92df-40bb-a9d6-ea6f151014e6"] }, Open ]], Cell[CellGroupData[{ -Cell[38274, 1077, 1109, 32, 94, "Input",ExpressionUUID->"7d5e0977-5bac-4f0b-84d8-60a1ab35a275"], -Cell[39386, 1111, 353, 9, 34, "Output",ExpressionUUID->"b988ffc4-7572-471d-8239-4575847456a9"], -Cell[39742, 1122, 383, 10, 34, "Output",ExpressionUUID->"b8ee1179-8690-4170-978a-4aecd92c574b"], -Cell[40128, 1134, 273, 6, 57, "Output",ExpressionUUID->"d63dc666-7e44-4d21-8d14-3e05799543fb"], -Cell[40404, 1142, 275, 5, 34, "Output",ExpressionUUID->"4fd282bd-3b9a-4ce5-8aa3-65d8486e87f6"] +Cell[40335, 1166, 1905, 48, 129, "Code",ExpressionUUID->"d22da0dd-f6c1-4ec2-9c0a-d342e4e587f3"], +Cell[42243, 1216, 426, 10, 34, "Output",ExpressionUUID->"cc271b25-2e33-4789-8505-58d7c6d45a79"], +Cell[42672, 1228, 422, 10, 34, "Output",ExpressionUUID->"c2d7d4a3-ab23-4adf-9c7c-a1a08cc514ed"], +Cell[43097, 1240, 445, 10, 34, "Output",ExpressionUUID->"de2a2937-73e4-409a-bda3-dce529de38a9"] }, Open ]], Cell[CellGroupData[{ -Cell[40716, 1152, 663, 20, 30, "Input",ExpressionUUID->"f8a04396-35d6-45a1-a0d2-fb838e0523ce"], -Cell[41382, 1174, 288, 8, 46, "Output",ExpressionUUID->"e3f4f8e2-7714-41c4-8b77-12ebd7cbf2ef"] +Cell[43579, 1255, 2081, 54, 91, "Code",ExpressionUUID->"af1435e5-10d6-484a-bbac-968a2283f2ae"], +Cell[45663, 1311, 762, 16, 34, "Output",ExpressionUUID->"f193fda5-76ee-44fe-9d80-065cf5814180"], +Cell[46428, 1329, 978, 22, 51, "Output",ExpressionUUID->"6b51c8f3-cf23-446f-b317-9ece5dd00c17"] }, Open ]] } ] From ee8f53310c27689dd345dfedd9cdc5e04fae9bfb Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Mon, 24 Feb 2025 10:13:54 +0100 Subject: [PATCH 10/18] fix cast to interpolation --- extras/ome_n3lo/test_interpolation.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/extras/ome_n3lo/test_interpolation.py b/extras/ome_n3lo/test_interpolation.py index 577dea1ae..c479134da 100644 --- a/extras/ome_n3lo/test_interpolation.py +++ b/extras/ome_n3lo/test_interpolation.py @@ -16,9 +16,9 @@ def ome_regular(entry, nf): def ome_local(entry, nf): if entry == "gg": - return Agg_asymptotic(0, nf) + return Agg_asymptotic(0, nf).real elif entry in ["qq_ns", "qq"]: - return Aqq_asymptotic(0, nf) + return Aqq_asymptotic(0, nf).real return 0 @@ -55,17 +55,17 @@ def test_moments(entry, N, nf): # TODO: some entries are passing other no... # np.testing.assert_allclose(ome_n, ome_x, rtol=4e-2, err_msg=f"{entry}, {nf}") - return ome_n, ome_x + return ome_n.real, ome_x if __name__ == "__main__": - N = 4 + N = 5.6788 entries = ["gg", "qq", "qq_ns", "gq", "qg", "Hg", "Hq"] for nf in [3, 4, 5]: results = [] for k in entries: results.append(test_moments(k, N, nf)) - df = pd.DataFrame(results, columns=["EKO", "Interpol"], index = entries, dtype=float) + df = pd.DataFrame(results, columns=["EKO", "Interpol"], index = entries) df["rel_diff"] = ((df.EKO - df.Interpol) / df.EKO) print("************************************") print(df) From e9ccce8ef6f3e527f3d89f5ba43b013482cdd8a4 Mon Sep 17 00:00:00 2001 From: Felix Hekhorn Date: Mon, 24 Feb 2025 15:09:48 +0200 Subject: [PATCH 11/18] Track ome interp output dir --- extras/ome_n3lo/x_space/.gitkeep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 extras/ome_n3lo/x_space/.gitkeep diff --git a/extras/ome_n3lo/x_space/.gitkeep b/extras/ome_n3lo/x_space/.gitkeep new file mode 100644 index 000000000..e69de29bb From 5298647822a570c8b1d23e7e551da7e545e32649 Mon Sep 17 00:00:00 2001 From: Giacomo Magni <39065935+giacomomagni@users.noreply.github.com> Date: Mon, 24 Feb 2025 16:32:25 +0100 Subject: [PATCH 12/18] Update extras/ome_n3lo/large_n_limit.py Co-authored-by: Felix Hekhorn --- extras/ome_n3lo/large_n_limit.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index 71c237146..2503115a3 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -3,9 +3,9 @@ The expansions are obtained using the notebook Agg_Aqq_largex_expansion.nb. We note that: - * the limit og :math:`A_{qq}` is the same for non-singlet like and singlet-like expansions. - I.e. the local and singular part are the same - * the :math:`A_{qq,ps}` temr is vanishing in the large-x limit, i.e. it's only regular. + * the limit of :math:`A_{qq}` is the same for valence-like and singlet-like expansions, + i.e. the local and singular parts are the same + * the :math:`A_{qq,ps}` term is vanishing in the large-x limit, i.e. it's only regular. """ from ekore.harmonics import S1 From 1a5f1d4049d891cfebbc5fa747344a4391ce581a Mon Sep 17 00:00:00 2001 From: Giacomo Magni <39065935+giacomomagni@users.noreply.github.com> Date: Mon, 24 Feb 2025 19:20:14 +0100 Subject: [PATCH 13/18] Update extras/ome_n3lo/convert_ome_xspace.py Co-authored-by: Felix Hekhorn --- extras/ome_n3lo/convert_ome_xspace.py | 1 - 1 file changed, 1 deletion(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 41a390c24..00fe97756 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -80,7 +80,6 @@ def integrand(u, x): epsabs=1e-12, epsrel=1e-6, limit=200, - full_output=1, )[0] ome_x.append(res) From a95dcec0b2696bf24c295c937d944826c805cb43 Mon Sep 17 00:00:00 2001 From: Giacomo Magni <39065935+giacomomagni@users.noreply.github.com> Date: Mon, 24 Feb 2025 19:27:26 +0100 Subject: [PATCH 14/18] Update extras/ome_n3lo/convert_ome_xspace.py Co-authored-by: Felix Hekhorn --- extras/ome_n3lo/convert_ome_xspace.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index 00fe97756..bcf02706b 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -1,4 +1,4 @@ -"""Dump a fast x-space grid of the N3LO transition matrix elements. +"""Dump a fast x-space grid of the N3LO transition matrix elements. The output file have the structure: x_grid, nf=3, nf=4, nf=5. """ From 00fad3a90b12b4ff2d49c32719d8e9aaa25a8c64 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Mon, 24 Feb 2025 19:32:19 +0100 Subject: [PATCH 15/18] apply comments --- extras/ome_n3lo/convert_ome_xspace.py | 11 +++-------- 1 file changed, 3 insertions(+), 8 deletions(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index bcf02706b..eaf251770 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -35,22 +35,20 @@ def compute_ome(nf, n, is_singlet): """Get the correct ome from eko.""" cache = c.reset() if is_singlet: - return as3.A_singlet(n, cache, nf, L=0) + return as3.A_singlet(n, cache, nf, L=LOG) else: - return as3.A_ns(n, cache, nf, L=0) + return as3.A_ns(n, cache, nf, L=LOG) def compute_xspace_ome(entry, nf, x_grid=XGRID): """Compute the x-space transition matrix element, returns A^3(x).""" - mellin_cut = 5e-2 + mellin_cut = 5e-3 is_singlet = "ns" not in entry def integrand(u, x): """Mellin inversion integrand.""" path = Path(u, np.log(x), is_singlet) integrand = path.prefactor * x ** (-path.n) * path.jac - if integrand == 0.0: - return 0.0 # compute the N space ome ome_n = compute_ome(nf, path.n, is_singlet) @@ -70,9 +68,6 @@ def integrand(u, x): # loop on xgrid with progressbar(x_grid) as bar: for x in bar: - if x == 1: - ome_x.append(0) - continue res = integrate.quad( lambda u: integrand(u, x), 0.5, From 1723ef08310e2b81fd0d4f0ce44c476d89b586d4 Mon Sep 17 00:00:00 2001 From: Giacomo Magni <39065935+giacomomagni@users.noreply.github.com> Date: Mon, 24 Feb 2025 19:35:45 +0100 Subject: [PATCH 16/18] Update extras/ome_n3lo/large_n_limit.py Co-authored-by: Felix Hekhorn --- extras/ome_n3lo/large_n_limit.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index 2503115a3..bf4bf5dbc 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -6,6 +6,9 @@ * the limit of :math:`A_{qq}` is the same for valence-like and singlet-like expansions, i.e. the local and singular parts are the same * the :math:`A_{qq,ps}` term is vanishing in the large-x limit, i.e. it's only regular. + +In the following we make use of a small trick, which is available due to complex continuation. Although we are interested in the large-N limit, we can obtain that by observing the small-N limit. It is :math:`S_1(0)=0` (by continuation), :math:`S_1(1)=1` and :math:`S_1(N\to\infty) = \ln(N) - \gamma_E`. + """ from ekore.harmonics import S1 From 07e8bf38d986152b6e99d5a914368bf21f12eea0 Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Mon, 24 Feb 2025 20:17:38 +0100 Subject: [PATCH 17/18] minor fixes --- extras/ome_n3lo/convert_ome_xspace.py | 2 +- extras/ome_n3lo/large_n_limit.py | 4 +++- extras/ome_n3lo/test_interpolation.py | 2 +- 3 files changed, 5 insertions(+), 3 deletions(-) diff --git a/extras/ome_n3lo/convert_ome_xspace.py b/extras/ome_n3lo/convert_ome_xspace.py index eaf251770..b57bc235f 100644 --- a/extras/ome_n3lo/convert_ome_xspace.py +++ b/extras/ome_n3lo/convert_ome_xspace.py @@ -42,7 +42,7 @@ def compute_ome(nf, n, is_singlet): def compute_xspace_ome(entry, nf, x_grid=XGRID): """Compute the x-space transition matrix element, returns A^3(x).""" - mellin_cut = 5e-3 + mellin_cut = 5e-2 is_singlet = "ns" not in entry def integrand(u, x): diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index bf4bf5dbc..cc1159f11 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -7,7 +7,9 @@ i.e. the local and singular parts are the same * the :math:`A_{qq,ps}` term is vanishing in the large-x limit, i.e. it's only regular. -In the following we make use of a small trick, which is available due to complex continuation. Although we are interested in the large-N limit, we can obtain that by observing the small-N limit. It is :math:`S_1(0)=0` (by continuation), :math:`S_1(1)=1` and :math:`S_1(N\to\infty) = \ln(N) - \gamma_E`. +In the following we make use of a small trick, which is available due to complex continuation. +Although we are interested in the large-N limit, we can obtain that by observing the small-N limit. +It is :math:`S_1(0)=0` (by continuation), :math:`S_1(1)=1` and :math:`S_1(N\to\infty) = \ln(N) - \gamma_E`. """ from ekore.harmonics import S1 diff --git a/extras/ome_n3lo/test_interpolation.py b/extras/ome_n3lo/test_interpolation.py index c479134da..237f7ee64 100644 --- a/extras/ome_n3lo/test_interpolation.py +++ b/extras/ome_n3lo/test_interpolation.py @@ -5,7 +5,7 @@ from scipy.integrate import quad from scipy.interpolate import CubicSpline -from convert_ome_xspace import LOG, MAP_ENTRIES, compute_ome +from convert_ome_xspace import MAP_ENTRIES, compute_ome from large_n_limit import Agg_asymptotic, Aqq_asymptotic From ffa351c03ecab98683b6dba43c3682d39798a66f Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Tue, 25 Feb 2025 08:59:50 +0100 Subject: [PATCH 18/18] pre-commit --- extras/ome_n3lo/large_n_limit.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/extras/ome_n3lo/large_n_limit.py b/extras/ome_n3lo/large_n_limit.py index cc1159f11..ce37f07cb 100644 --- a/extras/ome_n3lo/large_n_limit.py +++ b/extras/ome_n3lo/large_n_limit.py @@ -7,8 +7,8 @@ i.e. the local and singular parts are the same * the :math:`A_{qq,ps}` term is vanishing in the large-x limit, i.e. it's only regular. -In the following we make use of a small trick, which is available due to complex continuation. -Although we are interested in the large-N limit, we can obtain that by observing the small-N limit. +In the following we make use of a small trick, which is available due to complex continuation. +Although we are interested in the large-N limit, we can obtain that by observing the small-N limit. It is :math:`S_1(0)=0` (by continuation), :math:`S_1(1)=1` and :math:`S_1(N\to\infty) = \ln(N) - \gamma_E`. """ @@ -36,7 +36,7 @@ def Agg_asymptotic(n, nf): + 28.65462637880661 * nf ) agg_asy = ( - - 49.5041510989361 * (-14.442649813264895 + nf) * S1(n) + -49.5041510989361 * (-14.442649813264895 + nf) * S1(n) + 619.2420126046355 - 17.52475977636971 * nf )