Results of Hypergeometric Function II

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
15.10.E1	${\displaystyle{\displaystyle z(1-z)\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(c-(a+b+1)z\right)\frac{\mathrm{d}w}{\mathrm{d}z}-abw=0}}$ z(1-z)\deriv[2]{w}{z}+\left(c-(a+b+1)z\right)\deriv{w}{z}-abw = 0		z*(1 - z)*diff(w, [z$(2)])+(c -(a + b + 1)*z)*diff(w, z)- a*b*w = 0	z*(1 - z)*D[w, {z, 2}]+(c -(a + b + 1)*z)*D[w, z]- a*b*w == 0	Failure	Failure	Failed [300 / 300] Result: -1.948557159-1.125000000*I Test Values: {a = -3/2, b = -3/2, c = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: -1.948557159-1.125000000*I Test Values: {a = -3/2, b = -3/2, c = -3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.9742785792574935, -0.5624999999999999] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[w, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.9742785792574935, -0.5624999999999999] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[w, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10#Ex1	${\displaystyle{\displaystyle f_{1}(z)=F\left({a,b\atop c};z\right)}}$ f_{1}(z) = \hyperF@@{a}{b}{c}{z}		f[1](z) = hypergeom([a, b], [c], z)	Subscript[f, 1][z] == Hypergeometric2F1[a, b, c, z]	Failure	Failure	Failed [300 / 300] Result: .6425210462+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I} Result: -.7235043582+.8440762415*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250783, 0.5010855048154755] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.612671959171188, 0.4095791538693659] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10#Ex2	${\displaystyle{\displaystyle f_{2}(z)=z^{1-c}F\left({a-c+1,b-c+1\atop 2-c};z\right)}}$ f_{2}(z) = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}		f[2](z) = (z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [2 - c], z)	Subscript[f, 2][z] == (z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z]	Failure	Failure	Failed [300 / 300] Result: .5133103946-.4212876140*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I} Result: -.8527150098-.7873130176*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.09179462722314002, 0.01730691357980338] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.24971172372296968, -0.07419943736630628] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E3	${\displaystyle{\displaystyle\mathscr{W}\left\{f_{1}(z),f_{2}(z)\right\}=(1-c)z^{-c}(1-z)^{c-a-b-1}}}$ \Wronskian@{f_{1}(z),f_{2}(z)} = (1-c)z^{-c}(1-z)^{c-a-b-1}		(f[1](z))*diff(f[2](z), z)-diff(f[1](z), z)*(f[2](z)) = (1 - c)*(z)^(- c)*(1 - z)^(c - a - b - 1)	Wronskian[{Subscript[f, 1][z], Subscript[f, 2][z]}, z] == (1 - c)*(z)^(- c)*(1 - z)^(c - a - b - 1)	Translation Error	Translation Error	-	-
15.10#Ex3	${\displaystyle{\displaystyle f_{1}(z)=F\left({a,b\atop a+b+1-c};1-z\right)}}$ f_{1}(z) = \hyperF@@{a}{b}{a+b+1-c}{1-z}		f[1](z) = hypergeom([a, b], [a + b + 1 - c], 1 - z)	Subscript[f, 1][z] == Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z]	Failure	Failure	Failed [300 / 300] Result: -.1636283687-1.527783493*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I} Result: -1.529653773-1.893808897*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.9719632229411412, -1.2440609802148728] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.6304568719950316, -1.3355673311609824] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10#Ex4	${\displaystyle{\displaystyle f_{2}(z)=(1-z)^{c-a-b}F\left({c-a,c-b\atop c-a-b+1};1-z\right)}}$ f_{2}(z) = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z}		f[2](z) = (1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z)	Subscript[f, 2][z] == (1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z]	Failure	Failure	Failed [300 / 300] Result: .6425210462+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I} Result: -.7235043582+.8440762415*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250783, 0.5010855048154755] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.612671959171188, 0.4095791538693659] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E5	${\displaystyle{\displaystyle\mathscr{W}\left\{f_{1}(z),f_{2}(z)\right\}=(a+b-c)z^{-c}(1-z)^{c-a-b-1}}}$ \Wronskian@{f_{1}(z),f_{2}(z)} = (a+b-c)z^{-c}(1-z)^{c-a-b-1}		(f[1](z))*diff(f[2](z), z)-diff(f[1](z), z)*(f[2](z)) = (a + b - c)*(z)^(- c)*(1 - z)^(c - a - b - 1)	Wronskian[{Subscript[f, 1][z], Subscript[f, 2][z]}, z] == (a + b - c)*(z)^(- c)*(1 - z)^(c - a - b - 1)	Translation Error	Translation Error	-	-
15.10#Ex5	${\displaystyle{\displaystyle f_{1}(z)=z^{-a}F\left({a,a-c+1\atop a-b+1};\frac{1}{z}\right)}}$ f_{1}(z) = z^{-a}\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}		f[1](z) = (z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z))	Subscript[f, 1][z] == (z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]]	Failure	Failure	Failed [299 / 300] Result: .8440762415+.7235043582*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I} Result: -.5219491629+.3574789546*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [299 / 300] Result: Complex[0.40957915386936583, 0.6126719591711881] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.0680728029232561, 0.5211656082250784] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10#Ex6	${\displaystyle{\displaystyle f_{2}(z)=z^{-b}F\left({b,b-c+1\atop b-a+1};\frac{1}{z}\right)}}$ f_{2}(z) = z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}		f[2](z) = (z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z))	Subscript[f, 2][z] == (z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]]	Failure	Failure	Failed [299 / 300] Result: .8440762415+.7235043582*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I} Result: -.5219491629+.3574789546*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, f[2] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [299 / 300] Result: Complex[0.40957915386936583, 0.6126719591711881] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.0680728029232561, 0.5211656082250784] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[f, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E7	${\displaystyle{\displaystyle\mathscr{W}\left\{f_{1}(z),f_{2}(z)\right\}=(a-b)z^{-c}(z-1)^{c-a-b-1}}}$ \Wronskian@{f_{1}(z),f_{2}(z)} = (a-b)z^{-c}(z-1)^{c-a-b-1}		(f[1](z))*diff(f[2](z), z)-diff(f[1](z), z)*(f[2](z)) = (a - b)*(z)^(- c)*(z - 1)^(c - a - b - 1)	Wronskian[{Subscript[f, 1][z], Subscript[f, 2][z]}, z] == (a - b)*(z)^(- c)*(z - 1)^(c - a - b - 1)	Translation Error	Translation Error	-	-
15.10.E11	${\displaystyle{\displaystyle w_{1}(z)=F\left({a,b\atop c};z\right)}}$ w_{1}(z) = \hyperF@@{a}{b}{c}{z}		w[1](z) = hypergeom([a, b], [c], z)	Subscript[w, 1][z] == Hypergeometric2F1[a, b, c, z]	Failure	Failure	Failed [300 / 300] Result: .6425210462+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I} Result: -.7235043582+.8440762415*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250783, 0.5010855048154755] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.612671959171188, 0.4095791538693659] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E11	${\displaystyle{\displaystyle F\left({a,b\atop c};z\right)=(1-z)^{c-a-b}F\left({c-a,c-b\atop c};z\right)}}$ \hyperF@@{a}{b}{c}{z} = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z}		hypergeom([a, b], [c], z) = (1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c], z)	Hypergeometric2F1[a, b, c, z] == (1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c, z]	Failure	Successful	Skipped - Because timed out	Failed [49 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
15.10.E11	${\displaystyle{\displaystyle(1-z)^{c-a-b}F\left({c-a,c-b\atop c};z\right)=(1-z)^{-a}F\left({a,c-b\atop c};\frac{z}{z-1}\right)}}$ (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z} = (1-z)^{-a}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}}		(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c], z) = (1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1))	(1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c, z] == (1 - z)^(- a)* Hypergeometric2F1[a, c - b, c, Divide[z,z - 1]]	Failure	Failure	Skipped - Because timed out	Failed [83 / 300] Result: Complex[6.853625654927462, -2.5179782304346476*^-15] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 1.5], Rule[z, 1.5]} Result: Complex[8.642795715636197, -2.185751579730777*^-15] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 1.5], Rule[z, 2]} ... skip entries to safe data
15.10.E11	${\displaystyle{\displaystyle(1-z)^{-a}F\left({a,c-b\atop c};\frac{z}{z-1}\right)=(1-z)^{-b}F\left({c-a,b\atop c};\frac{z}{z-1}\right)}}$ (1-z)^{-a}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}} = (1-z)^{-b}\hyperF@@{c-a}{b}{c}{\frac{z}{z-1}}		(1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1)) = (1 - z)^(- b)* hypergeom([c - a, b], [c], (z)/(z - 1))	(1 - z)^(- a)* Hypergeometric2F1[a, c - b, c, Divide[z,z - 1]] == (1 - z)^(- b)* Hypergeometric2F1[c - a, b, c, Divide[z,z - 1]]	Failure	Failure	Failed [69 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [69 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E12	${\displaystyle{\displaystyle w_{2}(z)={z^{1-c}}F\left({a-c+1,b-c+1\atop 2-c};z\right)}}$ w_{2}(z) = {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}		w[2](z) = (z)^(1 - c)*hypergeom([a - c + 1, b - c + 1], [2 - c], z)	Subscript[w, 2][z] == (z)^(1 - c)*Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z]	Failure	Failure	Manual Skip!	Failed [300 / 300] Result: Complex[0.09179462722314002, 0.01730691357980338] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.24971172372296968, -0.07419943736630628] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E12	${\displaystyle{\displaystyle{z^{1-c}}F\left({a-c+1,b-c+1\atop 2-c};z\right)={z^{1-c}(1-z)^{c-a-b}}\*F\left({1-a,1-b\atop 2-c};z\right)}}$ {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z} = {z^{1-c}(1-z)^{c-a-b}}\*\hyperF@@{1-a}{1-b}{2-c}{z}		(z)^(1 - c)*hypergeom([a - c + 1, b - c + 1], [2 - c], z) = (z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [2 - c], z)	(z)^(1 - c)*Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z] == (z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, 2 - c, z]	Failure	Successful	Manual Skip!	Failed [49 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
15.10.E12	${\displaystyle{\displaystyle{z^{1-c}(1-z)^{c-a-b}}\*F\left({1-a,1-b\atop 2-c};z\right)={z^{1-c}(1-z)^{c-a-1}}\*F\left({a-c+1,1-b\atop 2-c};\frac{z}{z-1}\right)}}$ {z^{1-c}(1-z)^{c-a-b}}\*\hyperF@@{1-a}{1-b}{2-c}{z} = {z^{1-c}(1-z)^{c-a-1}}\*\hyperF@@{a-c+1}{1-b}{2-c}{\frac{z}{z-1}}		(z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [2 - c], z) = (z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([a - c + 1, 1 - b], [2 - c], (z)/(z - 1))	(z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, 2 - c, z] == (z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[a - c + 1, 1 - b, 2 - c, Divide[z,z - 1]]	Failure	Failure	Manual Skip!	Failed [74 / 300] Result: Complex[8.881784197001252*^-16, -5.5536036726979585] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, 1.5]} Result: Complex[1.7763568394002505*^-15, -15.707963267948971] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, 2]} ... skip entries to safe data
15.10.E12	${\displaystyle{\displaystyle{z^{1-c}(1-z)^{c-a-1}}\*F\left({a-c+1,1-b\atop 2-c};\frac{z}{z-1}\right)={z^{1-c}(1-z)^{c-b-1}}\*F\left({1-a,b-c+1\atop 2-c};\frac{z}{z-1}\right)}}$ {z^{1-c}(1-z)^{c-a-1}}\*\hyperF@@{a-c+1}{1-b}{2-c}{\frac{z}{z-1}} = {z^{1-c}(1-z)^{c-b-1}}\*\hyperF@@{1-a}{b-c+1}{2-c}{\frac{z}{z-1}}		(z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([a - c + 1, 1 - b], [2 - c], (z)/(z - 1)) = (z)^(1 - c)*(1 - z)^(c - b - 1)* hypergeom([1 - a, b - c + 1], [2 - c], (z)/(z - 1))	(z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[a - c + 1, 1 - b, 2 - c, Divide[z,z - 1]] == (z)^(1 - c)*(1 - z)^(c - b - 1)* Hypergeometric2F1[1 - a, b - c + 1, 2 - c, Divide[z,z - 1]]	Failure	Failure	Manual Skip!	Failed [69 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E13	${\displaystyle{\displaystyle w_{3}(z)=F\left({a,b\atop a+b-c+1};1-z\right)}}$ w_{3}(z) = \hyperF@@{a}{b}{a+b-c+1}{1-z}		w[3](z) = hypergeom([a, b], [a + b - c + 1], 1 - z)	Subscript[w, 3][z] == Hypergeometric2F1[a, b, a + b - c + 1, 1 - z]	Failure	Failure	Failed [300 / 300] Result: -.1636283687-1.527783493*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I} Result: -1.529653773-1.893808897*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[3] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.9719632229411412, -1.2440609802148728] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.6304568719950316, -1.3355673311609824] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E13	${\displaystyle{\displaystyle F\left({a,b\atop a+b-c+1};1-z\right)=z^{1-c}F\left({a-c+1,b-c+1\atop a+b-c+1};1-z\right)}}$ \hyperF@@{a}{b}{a+b-c+1}{1-z} = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{a+b-c+1}{1-z}		hypergeom([a, b], [a + b - c + 1], 1 - z) = (z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [a + b - c + 1], 1 - z)	Hypergeometric2F1[a, b, a + b - c + 1, 1 - z] == (z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, a + b - c + 1, 1 - z]	Failure	Successful	Skipped - Because timed out	Failed [70 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
15.10.E13	${\displaystyle{\displaystyle z^{1-c}F\left({a-c+1,b-c+1\atop a+b-c+1};1-z\right)=z^{-a}F\left({a,a-c+1\atop a+b-c+1};1-\frac{1}{z}\right)}}$ z^{1-c}\hyperF@@{a-c+1}{b-c+1}{a+b-c+1}{1-z} = z^{-a}\hyperF@@{a}{a-c+1}{a+b-c+1}{1-\frac{1}{z}}		(z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [a + b - c + 1], 1 - z) = (z)^(- a)* hypergeom([a, a - c + 1], [a + b - c + 1], 1 -(1)/(z))	(z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, a + b - c + 1, 1 - z] == (z)^(- a)* Hypergeometric2F1[a, a - c + 1, a + b - c + 1, 1 -Divide[1,z]]	Failure	Failure	Failed [56 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [57 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E13	${\displaystyle{\displaystyle z^{-a}F\left({a,a-c+1\atop a+b-c+1};1-\frac{1}{z}\right)=z^{-b}F\left({b,b-c+1\atop a+b-c+1};1-\frac{1}{z}\right)}}$ z^{-a}\hyperF@@{a}{a-c+1}{a+b-c+1}{1-\frac{1}{z}} = z^{-b}\hyperF@@{b}{b-c+1}{a+b-c+1}{1-\frac{1}{z}}		(z)^(- a)* hypergeom([a, a - c + 1], [a + b - c + 1], 1 -(1)/(z)) = (z)^(- b)* hypergeom([b, b - c + 1], [a + b - c + 1], 1 -(1)/(z))	(z)^(- a)* Hypergeometric2F1[a, a - c + 1, a + b - c + 1, 1 -Divide[1,z]] == (z)^(- b)* Hypergeometric2F1[b, b - c + 1, a + b - c + 1, 1 -Divide[1,z]]	Failure	Failure	Failed [70 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, c = -2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [71 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E14	${\displaystyle{\displaystyle w_{4}(z)=(1-z)^{c-a-b}F\left({c-a,c-b\atop c-a-b+1};1-z\right)}}$ w_{4}(z) = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z}		w[4](z) = (1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z)	Subscript[w, 4][z] == (1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z]	Failure	Failure	Failed [300 / 300] Result: .6425210462+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[4] = 1/2*3^(1/2)+1/2*I} Result: -.7235043582+.8440762415*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[4] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250783, 0.5010855048154755] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 4], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.612671959171188, 0.4095791538693659] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 4], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E14	${\displaystyle{\displaystyle(1-z)^{c-a-b}F\left({c-a,c-b\atop c-a-b+1};1-z\right)=z^{1-c}(1-z)^{c-a-b}F\left({1-a,1-b\atop c-a-b+1};1-z\right)}}$ (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z} = z^{1-c}(1-z)^{c-a-b}\hyperF@@{1-a}{1-b}{c-a-b+1}{1-z}		(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z) = (z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [c - a - b + 1], 1 - z)	(1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z] == (z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, c - a - b + 1, 1 - z]	Failure	Successful	Skipped - Because timed out	Failed [35 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
15.10.E14	${\displaystyle{\displaystyle z^{1-c}(1-z)^{c-a-b}F\left({1-a,1-b\atop c-a-b+1};1-z\right)=z^{a-c}(1-z)^{c-a-b}F\left({1-a,c-a\atop c-a-b+1};1-\frac{1}{z}\right)}}$ z^{1-c}(1-z)^{c-a-b}\hyperF@@{1-a}{1-b}{c-a-b+1}{1-z} = z^{a-c}(1-z)^{c-a-b}\hyperF@@{1-a}{c-a}{c-a-b+1}{1-\frac{1}{z}}		(z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [c - a - b + 1], 1 - z) = (z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [c - a - b + 1], 1 -(1)/(z))	(z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, c - a - b + 1, 1 - z] == (z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, c - a - b + 1, 1 -Divide[1,z]]	Failure	Failure	Skipped - Because timed out	Failed [35 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E14	${\displaystyle{\displaystyle z^{a-c}(1-z)^{c-a-b}F\left({1-a,c-a\atop c-a-b+1};1-\frac{1}{z}\right)=z^{b-c}(1-z)^{c-a-b}F\left({1-b,c-b\atop c-a-b+1};1-\frac{1}{z}\right)}}$ z^{a-c}(1-z)^{c-a-b}\hyperF@@{1-a}{c-a}{c-a-b+1}{1-\frac{1}{z}} = z^{b-c}(1-z)^{c-a-b}\hyperF@@{1-b}{c-b}{c-a-b+1}{1-\frac{1}{z}}		(z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [c - a - b + 1], 1 -(1)/(z)) = (z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [c - a - b + 1], 1 -(1)/(z))	(z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, c - a - b + 1, 1 -Divide[1,z]] == (z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, c - a - b + 1, 1 -Divide[1,z]]	Failure	Failure	Skipped - Because timed out	Failed [35 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E15	${\displaystyle{\displaystyle w_{5}(z)=e^{a\pi\mathrm{i}}z^{-a}\*F\left({a,a-c+1\atop a-b+1};\frac{1}{z}\right)}}$ w_{5}(z) = e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}		w[5](z) = exp(a*Pi*I)*(z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z))	Subscript[w, 5][z] == Exp[a*Pi*I]*(z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]]	Failure	Failure	Failed [300 / 300] Result: .6425210464+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[5] = 1/2*3^(1/2)+1/2*I} Result: -.7235043580+.8440762414*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[5] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250785, 0.5010855048154754] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 5], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.6126719591711882, 0.4095791538693657] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 5], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E15	${\displaystyle{\displaystyle e^{a\pi\mathrm{i}}z^{-a}\*F\left({a,a-c+1\atop a-b+1};\frac{1}{z}\right)=e^{(c-b)\pi\mathrm{i}}z^{b-c}(1-z)^{c-a-b}\*F\left({1-b,c-b\atop a-b+1};\frac{1}{z}\right)}}$ e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}} = e^{(c-b)\pi\iunit}z^{b-c}(1-z)^{c-a-b}\*\hyperF@@{1-b}{c-b}{a-b+1}{\frac{1}{z}}		exp(a*Pi*I)*(z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z)) = exp((c - b)*Pi*I)*(z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [a - b + 1], (1)/(z))	Exp[a*Pi*I]*(z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]] == Exp[(c - b)*Pi*I]*(z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, a - b + 1, Divide[1,z]]	Failure	Failure	Failed [177 / 300] Result: -.2921784397e-9-2.000000000*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2-1/2*I*3^(1/2)} Result: -4.961420107-2.055087494*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [177 / 300] Result: Complex[-1.139753528477389, -1.1397535284773888] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]]} Result: Complex[-3.3917924817064886, -0.8989459473483532] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]]} ... skip entries to safe data
15.10.E15	${\displaystyle{\displaystyle e^{(c-b)\pi\mathrm{i}}z^{b-c}(1-z)^{c-a-b}\*F\left({1-b,c-b\atop a-b+1};\frac{1}{z}\right)=(1-z)^{-a}F\left({a,c-b\atop a-b+1};\frac{1}{1-z}\right)}}$ e^{(c-b)\pi\iunit}z^{b-c}(1-z)^{c-a-b}\*\hyperF@@{1-b}{c-b}{a-b+1}{\frac{1}{z}} = (1-z)^{-a}\hyperF@@{a}{c-b}{a-b+1}{\frac{1}{1-z}}		exp((c - b)*Pi*I)*(z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [a - b + 1], (1)/(z)) = (1 - z)^(- a)* hypergeom([a, c - b], [a - b + 1], (1)/(1 - z))	Exp[(c - b)*Pi*I]*(z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, a - b + 1, Divide[1,z]] == (1 - z)^(- a)* Hypergeometric2F1[a, c - b, a - b + 1, Divide[1,1 - z]]	Failure	Failure	Failed [151 / 300] Result: -.3698264781e-8+6.010407640*I Test Values: {a = -3/2, b = -3/2, c = 3/2, z = 1/2} Result: -.1450299914e-9+.7071067812*I Test Values: {a = -3/2, b = -3/2, c = -1/2, z = 1/2} ... skip entries to safe data	Failed [151 / 300] Result: Complex[-7.360626478001693*^-16, 6.0104076400856545] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 1.5], Rule[z, 0.5]} Result: Complex[-1.232595164407831*^-32, 0.7071067811865476] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -0.5], Rule[z, 0.5]} ... skip entries to safe data
15.10.E15	${\displaystyle{\displaystyle(1-z)^{-a}F\left({a,c-b\atop a-b+1};\frac{1}{1-z}\right)=e^{(c-1)\pi\mathrm{i}}z^{1-c}(1-z)^{c-a-1}\*F\left({1-b,a-c+1\atop a-b+1};\frac{1}{1-z}\right)}}$ (1-z)^{-a}\hyperF@@{a}{c-b}{a-b+1}{\frac{1}{1-z}} = e^{(c-1)\pi\iunit}z^{1-c}(1-z)^{c-a-1}\*\hyperF@@{1-b}{a-c+1}{a-b+1}{\frac{1}{1-z}}		(1 - z)^(- a)* hypergeom([a, c - b], [a - b + 1], (1)/(1 - z)) = exp((c - 1)*Pi*I)*(z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([1 - b, a - c + 1], [a - b + 1], (1)/(1 - z))	(1 - z)^(- a)* Hypergeometric2F1[a, c - b, a - b + 1, Divide[1,1 - z]] == Exp[(c - 1)*Pi*I]*(z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[1 - b, a - c + 1, a - b + 1, Divide[1,1 - z]]	Failure	Failure	Failed [210 / 300] Result: .8062461775e-9+2.000000000*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2-1/2*I*3^(1/2)} Result: 4.961420108+2.055087494*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [210 / 300] Result: Complex[1.1397535284773888, 1.1397535284773896] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]]} Result: Complex[3.391792481706486, 0.8989459473483523] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]]} ... skip entries to safe data
15.10.E16	${\displaystyle{\displaystyle w_{6}(z)=e^{b\pi\mathrm{i}}z^{-b}F\left({b,b-c+1\atop b-a+1};\frac{1}{z}\right)}}$ w_{6}(z) = e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}		w[6](z) = exp(b*Pi*I)*(z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z))	Subscript[w, 6][z] == Exp[b*Pi*I]*(z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]]	Failure	Failure	Failed [300 / 300] Result: .6425210464+1.210101645*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[6] = 1/2*3^(1/2)+1/2*I} Result: -.7235043580+.8440762414*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I, w[6] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.2711656082250785, 0.5010855048154754] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 6], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.6126719591711882, 0.4095791538693657] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[w, 6], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.10.E16	${\displaystyle{\displaystyle e^{b\pi\mathrm{i}}z^{-b}F\left({b,b-c+1\atop b-a+1};\frac{1}{z}\right)=e^{(c-a)\pi\mathrm{i}}z^{a-c}(1-z)^{c-a-b}\*F\left({1-a,c-a\atop b-a+1};\frac{1}{z}\right)}}$ e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}} = e^{(c-a)\pi\iunit}z^{a-c}(1-z)^{c-a-b}\*\hyperF@@{1-a}{c-a}{b-a+1}{\frac{1}{z}}		exp(b*Pi*I)*(z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z)) = exp((c - a)*Pi*I)*(z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [b - a + 1], (1)/(z))	Exp[b*Pi*I]*(z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]] == Exp[(c - a)*Pi*I]*(z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, b - a + 1, Divide[1,z]]	Failure	Failure	Skipped - Because timed out	Failed [125 / 300] Result: Complex[-1.139753528477389, -1.1397535284773888] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]]} Result: Complex[-3.3917924817064886, -0.8989459473483532] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]]} ... skip entries to safe data
15.10.E16	${\displaystyle{\displaystyle e^{(c-a)\pi\mathrm{i}}z^{a-c}(1-z)^{c-a-b}\*F\left({1-a,c-a\atop b-a+1};\frac{1}{z}\right)=(1-z)^{-b}F\left({b,c-a\atop b-a+1};\frac{1}{1-z}\right)}}$ e^{(c-a)\pi\iunit}z^{a-c}(1-z)^{c-a-b}\*\hyperF@@{1-a}{c-a}{b-a+1}{\frac{1}{z}} = (1-z)^{-b}\hyperF@@{b}{c-a}{b-a+1}{\frac{1}{1-z}}		exp((c - a)*Pi*I)*(z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [b - a + 1], (1)/(z)) = (1 - z)^(- b)* hypergeom([b, c - a], [b - a + 1], (1)/(1 - z))	Exp[(c - a)*Pi*I]*(z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, b - a + 1, Divide[1,z]] == (1 - z)^(- b)* Hypergeometric2F1[b, c - a, b - a + 1, Divide[1,1 - z]]	Failure	Failure	Skipped - Because timed out	Failed [94 / 300] Result: Complex[-7.360626478001693*^-16, 6.0104076400856545] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, 1.5], Rule[z, 0.5]} Result: Complex[-1.232595164407831*^-32, 0.7071067811865476] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -0.5], Rule[z, 0.5]} ... skip entries to safe data
15.10.E16	${\displaystyle{\displaystyle(1-z)^{-b}F\left({b,c-a\atop b-a+1};\frac{1}{1-z}\right)=e^{(c-1)\pi\mathrm{i}}z^{1-c}(1-z)^{c-b-1}\*F\left({1-a,b-c+1\atop b-a+1};\frac{1}{1-z}\right)}}$ (1-z)^{-b}\hyperF@@{b}{c-a}{b-a+1}{\frac{1}{1-z}} = e^{(c-1)\pi\iunit}z^{1-c}(1-z)^{c-b-1}\*\hyperF@@{1-a}{b-c+1}{b-a+1}{\frac{1}{1-z}}		(1 - z)^(- b)* hypergeom([b, c - a], [b - a + 1], (1)/(1 - z)) = exp((c - 1)*Pi*I)*(z)^(1 - c)*(1 - z)^(c - b - 1)* hypergeom([1 - a, b - c + 1], [b - a + 1], (1)/(1 - z))	(1 - z)^(- b)* Hypergeometric2F1[b, c - a, b - a + 1, Divide[1,1 - z]] == Exp[(c - 1)*Pi*I]*(z)^(1 - c)*(1 - z)^(c - b - 1)* Hypergeometric2F1[1 - a, b - c + 1, b - a + 1, Divide[1,1 - z]]	Failure	Failure	Skipped - Because timed out	Failed [166 / 300] Result: Complex[1.1397535284773888, 1.1397535284773896] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]]} Result: Complex[3.391792481706486, 0.8989459473483523] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]]} ... skip entries to safe data
15.10.E17	${\displaystyle{\displaystyle w_{3}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(a+b-c+1\right)}{\Gamma\left(a-c+1\right)\Gamma\left(b-c+1\right)}w_{1}(z)+\frac{\Gamma\left(c-1\right)\Gamma\left(a+b-c+1\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}w_{2}(z)}}$ w_{3}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{a+b-c+1}}{\EulerGamma@{a-c+1}\EulerGamma@{b-c+1}}w_{1}(z)+\frac{\EulerGamma@{c-1}\EulerGamma@{a+b-c+1}}{\EulerGamma@{a}\EulerGamma@{b}}w_{2}(z)	${\displaystyle{\displaystyle\Re(1-c)>0,\Re(a+b-c+1)>0,\Re(a-c+1)>0,\Re(b-c+1)>0,\Re(c-1)>0,\Re a>0,\Re b>0}}$	w[3](z) = (GAMMA(1 - c)*GAMMA(a + b - c + 1))/(GAMMA(a - c + 1)*GAMMA(b - c + 1))*w[1](z)+(GAMMA(c - 1)*GAMMA(a + b - c + 1))/(GAMMA(a)*GAMMA(b))*w[2](z)	Subscript[w, 3][z] == Divide[Gamma[1 - c]*Gamma[a + b - c + 1],Gamma[a - c + 1]*Gamma[b - c + 1]]*Subscript[w, 1][z]+Divide[Gamma[c - 1]*Gamma[a + b - c + 1],Gamma[a]*Gamma[b]]*Subscript[w, 2][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E18	${\displaystyle{\displaystyle w_{4}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(c-a-b+1\right)}{\Gamma\left(1-a\right)\Gamma\left(1-b\right)}w_{1}(z)+\frac{\Gamma\left(c-1\right)\Gamma\left(c-a-b+1\right)}{\Gamma\left(c-a\right)\Gamma\left(c-b\right)}w_{2}(z)}}$ w_{4}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{c-a-b+1}}{\EulerGamma@{1-a}\EulerGamma@{1-b}}w_{1}(z)+\frac{\EulerGamma@{c-1}\EulerGamma@{c-a-b+1}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}w_{2}(z)	${\displaystyle{\displaystyle\Re(1-c)>0,\Re(c-a-b+1)>0,\Re(1-a)>0,\Re(1-b)>0,\Re(c-1)>0,\Re(c-a)>0,\Re(c-b)>0}}$	w[4](z) = (GAMMA(1 - c)*GAMMA(c - a - b + 1))/(GAMMA(1 - a)*GAMMA(1 - b))*w[1](z)+(GAMMA(c - 1)*GAMMA(c - a - b + 1))/(GAMMA(c - a)*GAMMA(c - b))*w[2](z)	Subscript[w, 4][z] == Divide[Gamma[1 - c]*Gamma[c - a - b + 1],Gamma[1 - a]*Gamma[1 - b]]*Subscript[w, 1][z]+Divide[Gamma[c - 1]*Gamma[c - a - b + 1],Gamma[c - a]*Gamma[c - b]]*Subscript[w, 2][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E19	${\displaystyle{\displaystyle w_{5}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(a-b+1\right)}{\Gamma\left(a-c+1\right)\Gamma\left(1-b\right)}w_{1}(z)+e^{(c-1)\pi\mathrm{i}}\frac{\Gamma\left(c-1\right)\Gamma\left(a-b+1\right)}{\Gamma\left(a\right)\Gamma\left(c-b\right)}w_{2}(z)}}$ w_{5}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{a-b+1}}{\EulerGamma@{a-c+1}\EulerGamma@{1-b}}w_{1}(z)+e^{(c-1)\pi\iunit}\frac{\EulerGamma@{c-1}\EulerGamma@{a-b+1}}{\EulerGamma@{a}\EulerGamma@{c-b}}w_{2}(z)	${\displaystyle{\displaystyle\Re(1-c)>0,\Re(a-b+1)>0,\Re(a-c+1)>0,\Re(1-b)>0,\Re(c-1)>0,\Re a>0,\Re(c-b)>0}}$	w[5](z) = (GAMMA(1 - c)*GAMMA(a - b + 1))/(GAMMA(a - c + 1)*GAMMA(1 - b))*w[1](z)+ exp((c - 1)*Pi*I)*(GAMMA(c - 1)*GAMMA(a - b + 1))/(GAMMA(a)*GAMMA(c - b))*w[2](z)	Subscript[w, 5][z] == Divide[Gamma[1 - c]*Gamma[a - b + 1],Gamma[a - c + 1]*Gamma[1 - b]]*Subscript[w, 1][z]+ Exp[(c - 1)*Pi*I]*Divide[Gamma[c - 1]*Gamma[a - b + 1],Gamma[a]*Gamma[c - b]]*Subscript[w, 2][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E20	${\displaystyle{\displaystyle w_{6}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(b-a+1\right)}{\Gamma\left(b-c+1\right)\Gamma\left(1-a\right)}w_{1}(z)+e^{(c-1)\pi\mathrm{i}}\frac{\Gamma\left(c-1\right)\Gamma\left(b-a+1\right)}{\Gamma\left(b\right)\Gamma\left(c-a\right)}w_{2}(z)}}$ w_{6}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{b-a+1}}{\EulerGamma@{b-c+1}\EulerGamma@{1-a}}w_{1}(z)+e^{(c-1)\pi\iunit}\frac{\EulerGamma@{c-1}\EulerGamma@{b-a+1}}{\EulerGamma@{b}\EulerGamma@{c-a}}w_{2}(z)	${\displaystyle{\displaystyle\Re(1-c)>0,\Re(b-a+1)>0,\Re(b-c+1)>0,\Re(1-a)>0,\Re(c-1)>0,\Re b>0,\Re(c-a)>0}}$	w[6](z) = (GAMMA(1 - c)*GAMMA(b - a + 1))/(GAMMA(b - c + 1)*GAMMA(1 - a))*w[1](z)+ exp((c - 1)*Pi*I)*(GAMMA(c - 1)*GAMMA(b - a + 1))/(GAMMA(b)*GAMMA(c - a))*w[2](z)	Subscript[w, 6][z] == Divide[Gamma[1 - c]*Gamma[b - a + 1],Gamma[b - c + 1]*Gamma[1 - a]]*Subscript[w, 1][z]+ Exp[(c - 1)*Pi*I]*Divide[Gamma[c - 1]*Gamma[b - a + 1],Gamma[b]*Gamma[c - a]]*Subscript[w, 2][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E21	${\displaystyle{\displaystyle w_{1}(z)=\frac{\Gamma\left(c\right)\Gamma\left(c-a-b\right)}{\Gamma\left(c-a\right)\Gamma\left(c-b\right)}w_{3}(z)+\frac{\Gamma\left(c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}w_{4}(z)}}$ w_{1}(z) = \frac{\EulerGamma@{c}\EulerGamma@{c-a-b}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}w_{3}(z)+\frac{\EulerGamma@{c}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{b}}w_{4}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(c-a-b)>0,\Re(c-a)>0,\Re(c-b)>0,\Re(a+b-c)>0,\Re a>0,\Re b>0}}$	w[1](z) = (GAMMA(c)*GAMMA(c - a - b))/(GAMMA(c - a)*GAMMA(c - b))*w[3](z)+(GAMMA(c)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(b))*w[4](z)	Subscript[w, 1][z] == Divide[Gamma[c]*Gamma[c - a - b],Gamma[c - a]*Gamma[c - b]]*Subscript[w, 3][z]+Divide[Gamma[c]*Gamma[a + b - c],Gamma[a]*Gamma[b]]*Subscript[w, 4][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E22	${\displaystyle{\displaystyle w_{2}(z)=\frac{\Gamma\left(2-c\right)\Gamma\left(c-a-b\right)}{\Gamma\left(1-a\right)\Gamma\left(1-b\right)}w_{3}(z)+\frac{\Gamma\left(2-c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a-c+1\right)\Gamma\left(b-c+1\right)}w_{4}(z)}}$ w_{2}(z) = \frac{\EulerGamma@{2-c}\EulerGamma@{c-a-b}}{\EulerGamma@{1-a}\EulerGamma@{1-b}}w_{3}(z)+\frac{\EulerGamma@{2-c}\EulerGamma@{a+b-c}}{\EulerGamma@{a-c+1}\EulerGamma@{b-c+1}}w_{4}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re(c-a-b)>0,\Re(1-a)>0,\Re(1-b)>0,\Re(a+b-c)>0,\Re(a-c+1)>0,\Re(b-c+1)>0}}$	w[2](z) = (GAMMA(2 - c)*GAMMA(c - a - b))/(GAMMA(1 - a)*GAMMA(1 - b))*w[3](z)+(GAMMA(2 - c)*GAMMA(a + b - c))/(GAMMA(a - c + 1)*GAMMA(b - c + 1))*w[4](z)	Subscript[w, 2][z] == Divide[Gamma[2 - c]*Gamma[c - a - b],Gamma[1 - a]*Gamma[1 - b]]*Subscript[w, 3][z]+Divide[Gamma[2 - c]*Gamma[a + b - c],Gamma[a - c + 1]*Gamma[b - c + 1]]*Subscript[w, 4][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E23	${\displaystyle{\displaystyle w_{5}(z)=e^{a\pi\mathrm{i}}\frac{\Gamma\left(a-b+1\right)\Gamma\left(c-a-b\right)}{\Gamma\left(1-b\right)\Gamma\left(c-b\right)}w_{3}(z)+e^{(c-b)\pi\mathrm{i}}\frac{\Gamma\left(a-b+1\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a\right)\Gamma\left(a-c+1\right)}w_{4}(z)}}$ w_{5}(z) = e^{a\pi\iunit}\frac{\EulerGamma@{a-b+1}\EulerGamma@{c-a-b}}{\EulerGamma@{1-b}\EulerGamma@{c-b}}w_{3}(z)+e^{(c-b)\pi\iunit}\frac{\EulerGamma@{a-b+1}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{a-c+1}}w_{4}(z)	${\displaystyle{\displaystyle\Re(a-b+1)>0,\Re(c-a-b)>0,\Re(1-b)>0,\Re(c-b)>0,\Re(a+b-c)>0,\Re a>0,\Re(a-c+1)>0}}$	w[5](z) = exp(a*Pi*I)*(GAMMA(a - b + 1)*GAMMA(c - a - b))/(GAMMA(1 - b)*GAMMA(c - b))*w[3](z)+ exp((c - b)*Pi*I)*(GAMMA(a - b + 1)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(a - c + 1))*w[4](z)	Subscript[w, 5][z] == Exp[a*Pi*I]*Divide[Gamma[a - b + 1]*Gamma[c - a - b],Gamma[1 - b]*Gamma[c - b]]*Subscript[w, 3][z]+ Exp[(c - b)*Pi*I]*Divide[Gamma[a - b + 1]*Gamma[a + b - c],Gamma[a]*Gamma[a - c + 1]]*Subscript[w, 4][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E24	${\displaystyle{\displaystyle w_{6}(z)=e^{b\pi\mathrm{i}}\frac{\Gamma\left(b-a+1\right)\Gamma\left(c-a-b\right)}{\Gamma\left(1-a\right)\Gamma\left(c-a\right)}w_{3}(z)+e^{(c-a)\pi\mathrm{i}}\frac{\Gamma\left(b-a+1\right)\Gamma\left(a+b-c\right)}{\Gamma\left(b\right)\Gamma\left(b-c+1\right)}w_{4}(z)}}$ w_{6}(z) = e^{b\pi\iunit}\frac{\EulerGamma@{b-a+1}\EulerGamma@{c-a-b}}{\EulerGamma@{1-a}\EulerGamma@{c-a}}w_{3}(z)+e^{(c-a)\pi\iunit}\frac{\EulerGamma@{b-a+1}\EulerGamma@{a+b-c}}{\EulerGamma@{b}\EulerGamma@{b-c+1}}w_{4}(z)	${\displaystyle{\displaystyle\Re(b-a+1)>0,\Re(c-a-b)>0,\Re(1-a)>0,\Re(c-a)>0,\Re(a+b-c)>0,\Re b>0,\Re(b-c+1)>0}}$	w[6](z) = exp(b*Pi*I)*(GAMMA(b - a + 1)*GAMMA(c - a - b))/(GAMMA(1 - a)*GAMMA(c - a))*w[3](z)+ exp((c - a)*Pi*I)*(GAMMA(b - a + 1)*GAMMA(a + b - c))/(GAMMA(b)*GAMMA(b - c + 1))*w[4](z)	Subscript[w, 6][z] == Exp[b*Pi*I]*Divide[Gamma[b - a + 1]*Gamma[c - a - b],Gamma[1 - a]*Gamma[c - a]]*Subscript[w, 3][z]+ Exp[(c - a)*Pi*I]*Divide[Gamma[b - a + 1]*Gamma[a + b - c],Gamma[b]*Gamma[b - c + 1]]*Subscript[w, 4][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E25	${\displaystyle{\displaystyle w_{1}(z)=\frac{\Gamma\left(c\right)\Gamma\left(b-a\right)}{\Gamma\left(b\right)\Gamma\left(c-a\right)}w_{5}(z)+\frac{\Gamma\left(c\right)\Gamma\left(a-b\right)}{\Gamma\left(a\right)\Gamma\left(c-b\right)}w_{6}(z)}}$ w_{1}(z) = \frac{\EulerGamma@{c}\EulerGamma@{b-a}}{\EulerGamma@{b}\EulerGamma@{c-a}}w_{5}(z)+\frac{\EulerGamma@{c}\EulerGamma@{a-b}}{\EulerGamma@{a}\EulerGamma@{c-b}}w_{6}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(b-a)>0,\Re b>0,\Re(c-a)>0,\Re(a-b)>0,\Re a>0,\Re(c-b)>0}}$	w[1](z) = (GAMMA(c)*GAMMA(b - a))/(GAMMA(b)*GAMMA(c - a))*w[5](z)+(GAMMA(c)*GAMMA(a - b))/(GAMMA(a)*GAMMA(c - b))*w[6](z)	Subscript[w, 1][z] == Divide[Gamma[c]*Gamma[b - a],Gamma[b]*Gamma[c - a]]*Subscript[w, 5][z]+Divide[Gamma[c]*Gamma[a - b],Gamma[a]*Gamma[c - b]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E26	${\displaystyle{\displaystyle w_{2}(z)=e^{(1-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(b-a\right)}{\Gamma\left(1-a\right)\Gamma\left(b-c+1\right)}w_{5}(z)+e^{(1-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(a-b\right)}{\Gamma\left(1-b\right)\Gamma\left(a-c+1\right)}w_{6}(z)}}$ w_{2}(z) = e^{(1-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b-a}}{\EulerGamma@{1-a}\EulerGamma@{b-c+1}}w_{5}(z)+e^{(1-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a-b}}{\EulerGamma@{1-b}\EulerGamma@{a-c+1}}w_{6}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re(b-a)>0,\Re(1-a)>0,\Re(b-c+1)>0,\Re(a-b)>0,\Re(1-b)>0,\Re(a-c+1)>0}}$	w[2](z) = exp((1 - c)*Pi*I)*(GAMMA(2 - c)*GAMMA(b - a))/(GAMMA(1 - a)*GAMMA(b - c + 1))*w[5](z)+ exp((1 - c)*Pi*I)*(GAMMA(2 - c)*GAMMA(a - b))/(GAMMA(1 - b)*GAMMA(a - c + 1))*w[6](z)	Subscript[w, 2][z] == Exp[(1 - c)*Pi*I]*Divide[Gamma[2 - c]*Gamma[b - a],Gamma[1 - a]*Gamma[b - c + 1]]*Subscript[w, 5][z]+ Exp[(1 - c)*Pi*I]*Divide[Gamma[2 - c]*Gamma[a - b],Gamma[1 - b]*Gamma[a - c + 1]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E27	${\displaystyle{\displaystyle w_{3}(z)=e^{-a\pi\mathrm{i}}\frac{\Gamma\left(a+b-c+1\right)\Gamma\left(b-a\right)}{\Gamma\left(b\right)\Gamma\left(b-c+1\right)}w_{5}(z)+e^{-b\pi\mathrm{i}}\frac{\Gamma\left(a+b-c+1\right)\Gamma\left(a-b\right)}{\Gamma\left(a\right)\Gamma\left(a-c+1\right)}w_{6}(z)}}$ w_{3}(z) = e^{-a\pi\iunit}\frac{\EulerGamma@{a+b-c+1}\EulerGamma@{b-a}}{\EulerGamma@{b}\EulerGamma@{b-c+1}}w_{5}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{a+b-c+1}\EulerGamma@{a-b}}{\EulerGamma@{a}\EulerGamma@{a-c+1}}w_{6}(z)	${\displaystyle{\displaystyle\Re(a+b-c+1)>0,\Re(b-a)>0,\Re b>0,\Re(b-c+1)>0,\Re(a-b)>0,\Re a>0,\Re(a-c+1)>0}}$	w[3](z) = exp(- a*Pi*I)*(GAMMA(a + b - c + 1)*GAMMA(b - a))/(GAMMA(b)*GAMMA(b - c + 1))*w[5](z)+ exp(- b*Pi*I)*(GAMMA(a + b - c + 1)*GAMMA(a - b))/(GAMMA(a)*GAMMA(a - c + 1))*w[6](z)	Subscript[w, 3][z] == Exp[- a*Pi*I]*Divide[Gamma[a + b - c + 1]*Gamma[b - a],Gamma[b]*Gamma[b - c + 1]]*Subscript[w, 5][z]+ Exp[- b*Pi*I]*Divide[Gamma[a + b - c + 1]*Gamma[a - b],Gamma[a]*Gamma[a - c + 1]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E28	${\displaystyle{\displaystyle w_{4}(z)=e^{(b-c)\pi\mathrm{i}}\frac{\Gamma\left(c-a-b+1\right)\Gamma\left(b-a\right)}{\Gamma\left(1-a\right)\Gamma\left(c-a\right)}w_{5}(z)+e^{(a-c)\pi\mathrm{i}}\frac{\Gamma\left(c-a-b+1\right)\Gamma\left(a-b\right)}{\Gamma\left(1-b\right)\Gamma\left(c-b\right)}w_{6}(z)}}$ w_{4}(z) = e^{(b-c)\pi\iunit}\frac{\EulerGamma@{c-a-b+1}\EulerGamma@{b-a}}{\EulerGamma@{1-a}\EulerGamma@{c-a}}w_{5}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{c-a-b+1}\EulerGamma@{a-b}}{\EulerGamma@{1-b}\EulerGamma@{c-b}}w_{6}(z)	${\displaystyle{\displaystyle\Re(c-a-b+1)>0,\Re(b-a)>0,\Re(1-a)>0,\Re(c-a)>0,\Re(a-b)>0,\Re(1-b)>0,\Re(c-b)>0}}$	w[4](z) = exp((b - c)*Pi*I)*(GAMMA(c - a - b + 1)*GAMMA(b - a))/(GAMMA(1 - a)*GAMMA(c - a))*w[5](z)+ exp((a - c)*Pi*I)*(GAMMA(c - a - b + 1)*GAMMA(a - b))/(GAMMA(1 - b)*GAMMA(c - b))*w[6](z)	Subscript[w, 4][z] == Exp[(b - c)*Pi*I]*Divide[Gamma[c - a - b + 1]*Gamma[b - a],Gamma[1 - a]*Gamma[c - a]]*Subscript[w, 5][z]+ Exp[(a - c)*Pi*I]*Divide[Gamma[c - a - b + 1]*Gamma[a - b],Gamma[1 - b]*Gamma[c - b]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E29	${\displaystyle{\displaystyle w_{1}(z)=e^{b\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(a-c+1\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(c-b\right)}w_{3}(z)+e^{(b-c)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(a-c+1\right)}{\Gamma\left(b\right)\Gamma\left(a-b+1\right)}w_{5}(z)}}$ w_{1}(z) = e^{b\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{a-c+1}}{\EulerGamma@{a+b-c+1}\EulerGamma@{c-b}}w_{3}(z)+e^{(b-c)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{a-c+1}}{\EulerGamma@{b}\EulerGamma@{a-b+1}}w_{5}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(a-c+1)>0,\Re(a+b-c+1)>0,\Re(c-b)>0,\Re b>0,\Re(a-b+1)>0}}$	w[1](z) = exp(b*Pi*I)*(GAMMA(c)*GAMMA(a - c + 1))/(GAMMA(a + b - c + 1)*GAMMA(c - b))*w[3](z)+ exp((b - c)*Pi*I)*(GAMMA(c)*GAMMA(a - c + 1))/(GAMMA(b)*GAMMA(a - b + 1))*w[5](z)	Subscript[w, 1][z] == Exp[b*Pi*I]*Divide[Gamma[c]*Gamma[a - c + 1],Gamma[a + b - c + 1]*Gamma[c - b]]*Subscript[w, 3][z]+ Exp[(b - c)*Pi*I]*Divide[Gamma[c]*Gamma[a - c + 1],Gamma[b]*Gamma[a - b + 1]]*Subscript[w, 5][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E30	${\displaystyle{\displaystyle w_{1}(z)=e^{a\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(b-c+1\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(c-a\right)}w_{3}(z)+e^{(a-c)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(b-c+1\right)}{\Gamma\left(a\right)\Gamma\left(b-a+1\right)}w_{6}(z)}}$ w_{1}(z) = e^{a\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{b-c+1}}{\EulerGamma@{a+b-c+1}\EulerGamma@{c-a}}w_{3}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{b-c+1}}{\EulerGamma@{a}\EulerGamma@{b-a+1}}w_{6}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(b-c+1)>0,\Re(a+b-c+1)>0,\Re(c-a)>0,\Re a>0,\Re(b-a+1)>0}}$	w[1](z) = exp(a*Pi*I)*(GAMMA(c)*GAMMA(b - c + 1))/(GAMMA(a + b - c + 1)*GAMMA(c - a))*w[3](z)+ exp((a - c)*Pi*I)*(GAMMA(c)*GAMMA(b - c + 1))/(GAMMA(a)*GAMMA(b - a + 1))*w[6](z)	Subscript[w, 1][z] == Exp[a*Pi*I]*Divide[Gamma[c]*Gamma[b - c + 1],Gamma[a + b - c + 1]*Gamma[c - a]]*Subscript[w, 3][z]+ Exp[(a - c)*Pi*I]*Divide[Gamma[c]*Gamma[b - c + 1],Gamma[a]*Gamma[b - a + 1]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E31	${\displaystyle{\displaystyle w_{2}(z)=e^{(b-c+1)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(a\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(1-b\right)}w_{3}(z)+e^{(b-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(a\right)}{\Gamma\left(a-b+1\right)\Gamma\left(b-c+1\right)}w_{5}(z)}}$ w_{2}(z) = e^{(b-c+1)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a}}{\EulerGamma@{a+b-c+1}\EulerGamma@{1-b}}w_{3}(z)+e^{(b-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a}}{\EulerGamma@{a-b+1}\EulerGamma@{b-c+1}}w_{5}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re a>0,\Re(a+b-c+1)>0,\Re(1-b)>0,\Re(a-b+1)>0,\Re(b-c+1)>0}}$	w[2](z) = exp((b - c + 1)*Pi*I)*(GAMMA(2 - c)*GAMMA(a))/(GAMMA(a + b - c + 1)*GAMMA(1 - b))*w[3](z)+ exp((b - c)*Pi*I)*(GAMMA(2 - c)*GAMMA(a))/(GAMMA(a - b + 1)*GAMMA(b - c + 1))*w[5](z)	Subscript[w, 2][z] == Exp[(b - c + 1)*Pi*I]*Divide[Gamma[2 - c]*Gamma[a],Gamma[a + b - c + 1]*Gamma[1 - b]]*Subscript[w, 3][z]+ Exp[(b - c)*Pi*I]*Divide[Gamma[2 - c]*Gamma[a],Gamma[a - b + 1]*Gamma[b - c + 1]]*Subscript[w, 5][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E32	${\displaystyle{\displaystyle w_{2}(z)=e^{(a-c+1)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(b\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(1-a\right)}w_{3}(z)+e^{(a-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(b\right)}{\Gamma\left(b-a+1\right)\Gamma\left(a-c+1\right)}w_{6}(z)}}$ w_{2}(z) = e^{(a-c+1)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b}}{\EulerGamma@{a+b-c+1}\EulerGamma@{1-a}}w_{3}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b}}{\EulerGamma@{b-a+1}\EulerGamma@{a-c+1}}w_{6}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re b>0,\Re(a+b-c+1)>0,\Re(1-a)>0,\Re(b-a+1)>0,\Re(a-c+1)>0}}$	w[2](z) = exp((a - c + 1)*Pi*I)*(GAMMA(2 - c)*GAMMA(b))/(GAMMA(a + b - c + 1)*GAMMA(1 - a))*w[3](z)+ exp((a - c)*Pi*I)*(GAMMA(2 - c)*GAMMA(b))/(GAMMA(b - a + 1)*GAMMA(a - c + 1))*w[6](z)	Subscript[w, 2][z] == Exp[(a - c + 1)*Pi*I]*Divide[Gamma[2 - c]*Gamma[b],Gamma[a + b - c + 1]*Gamma[1 - a]]*Subscript[w, 3][z]+ Exp[(a - c)*Pi*I]*Divide[Gamma[2 - c]*Gamma[b],Gamma[b - a + 1]*Gamma[a - c + 1]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E33	${\displaystyle{\displaystyle w_{1}(z)=e^{(c-a)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-b\right)}{\Gamma\left(a\right)\Gamma\left(c-a-b+1\right)}w_{4}(z)+e^{-a\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-b\right)}{\Gamma\left(a-b+1\right)\Gamma\left(c-a\right)}w_{5}(z)}}$ w_{1}(z) = e^{(c-a)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-b}}{\EulerGamma@{a}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-a\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-b}}{\EulerGamma@{a-b+1}\EulerGamma@{c-a}}w_{5}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(1-b)>0,\Re a>0,\Re(c-a-b+1)>0,\Re(a-b+1)>0,\Re(c-a)>0}}$	w[1](z) = exp((c - a)*Pi*I)*(GAMMA(c)*GAMMA(1 - b))/(GAMMA(a)*GAMMA(c - a - b + 1))*w[4](z)+ exp(- a*Pi*I)*(GAMMA(c)*GAMMA(1 - b))/(GAMMA(a - b + 1)*GAMMA(c - a))*w[5](z)	Subscript[w, 1][z] == Exp[(c - a)*Pi*I]*Divide[Gamma[c]*Gamma[1 - b],Gamma[a]*Gamma[c - a - b + 1]]*Subscript[w, 4][z]+ Exp[- a*Pi*I]*Divide[Gamma[c]*Gamma[1 - b],Gamma[a - b + 1]*Gamma[c - a]]*Subscript[w, 5][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E34	${\displaystyle{\displaystyle w_{1}(z)=e^{(c-b)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-a\right)}{\Gamma\left(b\right)\Gamma\left(c-a-b+1\right)}w_{4}(z)+e^{-b\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-a\right)}{\Gamma\left(b-a+1\right)\Gamma\left(c-b\right)}w_{6}(z)}}$ w_{1}(z) = e^{(c-b)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-a}}{\EulerGamma@{b}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-a}}{\EulerGamma@{b-a+1}\EulerGamma@{c-b}}w_{6}(z)	${\displaystyle{\displaystyle\Re c>0,\Re(1-a)>0,\Re b>0,\Re(c-a-b+1)>0,\Re(b-a+1)>0,\Re(c-b)>0}}$	w[1](z) = exp((c - b)*Pi*I)*(GAMMA(c)*GAMMA(1 - a))/(GAMMA(b)*GAMMA(c - a - b + 1))*w[4](z)+ exp(- b*Pi*I)*(GAMMA(c)*GAMMA(1 - a))/(GAMMA(b - a + 1)*GAMMA(c - b))*w[6](z)	Subscript[w, 1][z] == Exp[(c - b)*Pi*I]*Divide[Gamma[c]*Gamma[1 - a],Gamma[b]*Gamma[c - a - b + 1]]*Subscript[w, 4][z]+ Exp[- b*Pi*I]*Divide[Gamma[c]*Gamma[1 - a],Gamma[b - a + 1]*Gamma[c - b]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E35	${\displaystyle{\displaystyle w_{2}(z)=e^{(1-a)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-b\right)}{\Gamma\left(a-c+1\right)\Gamma\left(c-a-b+1\right)}w_{4}(z)+e^{-a\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-b\right)}{\Gamma\left(a-b+1\right)\Gamma\left(1-a\right)}w_{5}(z)}}$ w_{2}(z) = e^{(1-a)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-b}}{\EulerGamma@{a-c+1}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-a\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-b}}{\EulerGamma@{a-b+1}\EulerGamma@{1-a}}w_{5}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re(c-b)>0,\Re(a-c+1)>0,\Re(c-a-b+1)>0,\Re(a-b+1)>0,\Re(1-a)>0}}$	w[2](z) = exp((1 - a)*Pi*I)*(GAMMA(2 - c)*GAMMA(c - b))/(GAMMA(a - c + 1)*GAMMA(c - a - b + 1))*w[4](z)+ exp(- a*Pi*I)*(GAMMA(2 - c)*GAMMA(c - b))/(GAMMA(a - b + 1)*GAMMA(1 - a))*w[5](z)	Subscript[w, 2][z] == Exp[(1 - a)*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - b],Gamma[a - c + 1]*Gamma[c - a - b + 1]]*Subscript[w, 4][z]+ Exp[- a*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - b],Gamma[a - b + 1]*Gamma[1 - a]]*Subscript[w, 5][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.10.E36	${\displaystyle{\displaystyle w_{2}(z)=e^{(1-b)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-a\right)}{\Gamma\left(b-c+1\right)\Gamma\left(c-a-b+1\right)}w_{4}(z)+e^{-b\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-a\right)}{\Gamma\left(b-a+1\right)\Gamma\left(1-b\right)}w_{6}(z)}}$ w_{2}(z) = e^{(1-b)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-a}}{\EulerGamma@{b-c+1}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-a}}{\EulerGamma@{b-a+1}\EulerGamma@{1-b}}w_{6}(z)	${\displaystyle{\displaystyle\Re(2-c)>0,\Re(c-a)>0,\Re(b-c+1)>0,\Re(c-a-b+1)>0,\Re(b-a+1)>0,\Re(1-b)>0}}$	w[2](z) = exp((1 - b)*Pi*I)*(GAMMA(2 - c)*GAMMA(c - a))/(GAMMA(b - c + 1)*GAMMA(c - a - b + 1))*w[4](z)+ exp(- b*Pi*I)*(GAMMA(2 - c)*GAMMA(c - a))/(GAMMA(b - a + 1)*GAMMA(1 - b))*w[6](z)	Subscript[w, 2][z] == Exp[(1 - b)*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - a],Gamma[b - c + 1]*Gamma[c - a - b + 1]]*Subscript[w, 4][z]+ Exp[- b*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - a],Gamma[b - a + 1]*Gamma[1 - b]]*Subscript[w, 6][z]	Failure	Failure	Manual Skip!	Skipped - Because timed out
15.11.E2	${\displaystyle{\displaystyle a_{1}+a_{2}+b_{1}+b_{2}+c_{1}+c_{2}=1}}$ a_{1}+a_{2}+b_{1}+b_{2}+c_{1}+c_{2} = 1		a[1]+ a[2]+ b[1]+ b[2]+ c[1]+ c[2] = 1	Subscript[a, 1]+ Subscript[a, 2]+ Subscript[b, 1]+ Subscript[b, 2]+ Subscript[c, 1]+ Subscript[c, 2] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
15.11.E5	${\displaystyle{\displaystyle t=\ifrac{(\kappa z+\lambda)}{(\mu z+\nu)}}}$ t = \ifrac{(\kappa z+\lambda)}{(\mu z+\nu)}		t = (kappa*z + lambda)/(mu*z + nu)	t == Divide[\[Kappa]*z + \[Lambda],\[Mu]*z + \[Nu]]	Skipped - no semantic math	Skipped - no semantic math	-	-
15.12.E1	${\displaystyle{\displaystyle\alpha_{+}=\operatorname{arctan}\left(\frac{\operatorname{ph}z-\operatorname{ph}\left(1-z\right)-\pi}{\ln|1-z^{-1}|}\right)}}$ \alpha_{+} = \atan@{\frac{\phase@@{z}-\phase@{1-z}-\pi}{\ln@@{|1-z^{-1}|}}}		alpha[+] = arctan((argument(z)- argument(1 - z)- Pi)/(ln(abs(1 - (z)^(- 1)))))	Subscript[\[Alpha], +] == ArcTan[Divide[Arg[z]- Arg[1 - z]- Pi,Log[Abs[1 - (z)^(- 1)]]]]	Error	Failure	-	Error
15.12.E1	${\displaystyle{\displaystyle\alpha_{-}=\operatorname{arctan}\left(\frac{\operatorname{ph}z-\operatorname{ph}\left(1-z\right)+\pi}{\ln|1-z^{-1}|}\right)}}$ \alpha_{-} = \atan@{\frac{\phase@@{z}-\phase@{1-z}+\pi}{\ln@@{|1-z^{-1}|}}}		alpha[-] = arctan((argument(z)- argument(1 - z)+ Pi)/(ln(abs(1 - (z)^(- 1)))))	Subscript[\[Alpha], -] == ArcTan[Divide[Arg[z]- Arg[1 - z]+ Pi,Log[Abs[1 - (z)^(- 1)]]]]	Error	Failure	-	Error
15.12.E4	${\displaystyle{\displaystyle\left(\frac{e^{t}-1}{t}\right)^{b-1}e^{t(1-c)}\left(1-z+ze^{-t}\right)^{-a}=\sum_{s=0}^{\infty}q_{s}(z)t^{s}}}$ \left(\frac{e^{t}-1}{t}\right)^{b-1}e^{t(1-c)}\left(1-z+ze^{-t}\right)^{-a} = \sum_{s=0}^{\infty}q_{s}(z)t^{s}		((exp(t)- 1)/(t))^(b - 1)* exp(t*(1 - c))*(1 - z + z*exp(- t))^(- a) = sum(q[s](z)* (t)^(s), s = 0..infinity)	(Divide[Exp[t]- 1,t])^(b - 1)* Exp[t*(1 - c)]*(1 - z + z*Exp[- t])^(- a) == Sum[Subscript[q, s][z]* (t)^(s), {s, 0, Infinity}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
15.12.E6	${\displaystyle{\displaystyle\zeta=\operatorname{arccosh}z}}$ \zeta = \acosh@@{z}		zeta = arccosh(z)	\[Zeta] == ArcCosh[z]	Failure	Failure	Failed [70 / 70] Result: .2075464554-.2853981632*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I} Result: -1.158478949+.806272408e-1*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [70 / 70] Result: Complex[0.1612451656432845, -0.8901042143273741] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.5217675362489347, -0.7070915124351547] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.12.E8	${\displaystyle{\displaystyle\alpha=\left(-2\ln\left(1-\left(\frac{z-1}{z+1}\right)^{2}\right)\right)^{1/2}}}$ \alpha = \left(-2\ln@{1-\left(\frac{z-1}{z+1}\right)^{2}}\right)^{1/2}		alpha = (- 2*ln(1 -((z - 1)/(z + 1))^(2)))^(1/2)	\[Alpha] == (- 2*Log[1 -(Divide[z - 1,z + 1])^(2)])^(1/2)	Failure	Failure	Failed [21 / 21] Result: 1.500000000-.3723881428*I Test Values: {alpha = 3/2, z = 1/2*3^(1/2)+1/2*I} Result: 1.500000000-1.665109222*I Test Values: {alpha = 3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.0067817778628907, 0.36121951329018404] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[α, 1.5]} Result: Complex[0.006781777862890637, 0.36121951329018404] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[α, 0.5]} ... skip entries to safe data
15.12.E10	${\displaystyle{\displaystyle\zeta=\operatorname{arccosh}\left(\tfrac{1}{4}z-1\right)}}$ \zeta = \acosh@{\tfrac{1}{4}z-1}		zeta = arccosh((1)/(4)*z - 1)	\[Zeta] == ArcCosh[Divide[1,4]*z - 1]	Failure	Failure	Failed [70 / 70] Result: .6717322583-1.947968998*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I} Result: -.6942931457-1.581943594*I Test Values: {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [70 / 70] Result: Complex[0.29977340809145847, -2.404910564859421] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.3832392938007607, -2.221897862967202] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.12.E11	${\displaystyle{\displaystyle\beta=\left(-\frac{3}{2}\zeta+\frac{9}{4}\ln\left(\frac{2+e^{\zeta}}{2+e^{-\zeta}}\right)\right)^{1/3}}}$ \beta = \left(-\frac{3}{2}\zeta+\frac{9}{4}\ln@{\frac{2+e^{\zeta}}{2+e^{-\zeta}}}\right)^{1/3}		beta = (-(3)/(2)*zeta +(9)/(4)*ln((2 + exp(zeta))/(2 + exp(- zeta))))^(1/3)	\[Beta] == (-Divide[3,2]*\[Zeta]+Divide[9,4]*Log[Divide[2 + Exp[\[Zeta]],2 + Exp[- \[Zeta]]]])^(1/3)	Failure	Failure	Failed [30 / 30] Result: 1.169986459-.1804633349*I Test Values: {beta = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: 1.113419726-.9637472295e-2*I Test Values: {beta = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [30 / 30] Result: Complex[1.3347889019926584, -0.09407633084828147] Test Values: {Rule[β, 1.5], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.308560321923405, -0.0011617388335202368] Test Values: {Rule[β, 1.5], Rule[ζ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.12#Ex1	${\displaystyle{\displaystyle a_{0}(\zeta)=\tfrac{1}{2}G_{0}(\beta)+\tfrac{1}{2}G_{0}(-\beta)}}$ a_{0}(\zeta) = \tfrac{1}{2}G_{0}(\beta)+\tfrac{1}{2}G_{0}(-\beta)		a[0](zeta) = (1)/(2)*G[0](beta)+(1)/(2)*G[0](- beta)	Subscript[a, 0][\[Zeta]] == Divide[1,2]*Subscript[G, 0][\[Beta]]+Divide[1,2]*Subscript[G, 0][- \[Beta]]	Skipped - no semantic math	Skipped - no semantic math	-	-
15.12#Ex2	${\displaystyle{\displaystyle a_{1}(\zeta)=\left(\tfrac{1}{2}G_{0}(\beta)-\tfrac{1}{2}G_{0}(-\beta)\right)/\beta}}$ a_{1}(\zeta) = \left(\tfrac{1}{2}G_{0}(\beta)-\tfrac{1}{2}G_{0}(-\beta)\right)/\beta		a[1](zeta) = ((1)/(2)*G[0](beta)-(1)/(2)*G[0](- beta))/beta	Subscript[a, 1][\[Zeta]] == (Divide[1,2]*Subscript[G, 0][\[Beta]]-Divide[1,2]*Subscript[G, 0][- \[Beta]])/\[Beta]	Skipped - no semantic math	Skipped - no semantic math	-	-
15.12.E13	${\displaystyle{\displaystyle G_{0}(+\beta)=\left(2+e^{+\zeta}\right)^{c-b-(\ifrac{1}{2})}\left(1+e^{+\zeta}\right)^{a-c+(\ifrac{1}{2})}\left(z-1-e^{+\zeta}\right)^{-a+(\ifrac{1}{2})}\sqrt{\frac{\beta}{e^{\zeta}-e^{-\zeta}}}}}$ G_{0}(+\beta) = \left(2+e^{+\zeta}\right)^{c-b-(\ifrac{1}{2})}\left(1+e^{+\zeta}\right)^{a-c+(\ifrac{1}{2})}\left(z-1-e^{+\zeta}\right)^{-a+(\ifrac{1}{2})}\sqrt{\frac{\beta}{e^{\zeta}-e^{-\zeta}}}		G[0](+ beta) = (2 + exp(+ zeta))^(c - b -((1)/(2)))*(1 + exp(+ zeta))^(a - c +((1)/(2)))*(z - 1 - exp(+ zeta))^(- a +((1)/(2)))*sqrt((beta)/(exp(zeta)- exp(- zeta)))	Subscript[G, 0][+ \[Beta]] == (2 + Exp[+ \[Zeta]])^(c - b -(Divide[1,2]))*(1 + Exp[+ \[Zeta]])^(a - c +(Divide[1,2]))*(z - 1 - Exp[+ \[Zeta]])^(- a +(Divide[1,2]))*Sqrt[Divide[\[Beta],Exp[\[Zeta]]- Exp[- \[Zeta]]]]	Skipped - no semantic math	Skipped - no semantic math	-	-
15.14.E1	${\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c};-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma\left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s\right)}}}$ \int_{0}^{\infty}x^{s-1}\hyperOlverF@@{a}{b}{c}{-x}\diff{x} = \frac{\EulerGamma@{s}\EulerGamma@{a-s}\EulerGamma@{b-s}}{\EulerGamma@{a}\EulerGamma@{b}\EulerGamma@{c-s}}	${\displaystyle{\displaystyle\min(\Re a>\Re s,\Re b)>\Re s,\Re s>0,\Re(a-s)>0,\Re(b-s)>0,\Re a>0,\Re b>0,\Re(c-s)>0,|(-x)|<1,\Re(c+s)>0}}$	int((x)^(s - 1)* hypergeom([a, b], [c], - x)/GAMMA(c), x = 0..infinity) = (GAMMA(s)*GAMMA(a - s)*GAMMA(b - s))/(GAMMA(a)*GAMMA(b)*GAMMA(c - s))	Integrate[(x)^(s - 1)* Hypergeometric2F1Regularized[a, b, c, - x], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[s]*Gamma[a - s]*Gamma[b - s],Gamma[a]*Gamma[b]*Gamma[c - s]]	Successful	Aborted	-	Skipped - Because timed out
15.15.E1	${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};\frac{1}{z}\right)=\left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\mathbf{F}\left({-s,b\atop c};\frac{1}{z_{0}}\right)\left(1-\frac{z}{z_{0}}\right)^{-s}}}$ \hyperOlverF@@{a}{b}{c}{\frac{1}{z}} = \left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\hyperOlverF@@{-s}{b}{c}{\frac{1}{z_{0}}}\left(1-\frac{z}{z_{0}}\right)^{-s}		hypergeom([a, b], [c], (1)/(z))/GAMMA(c) = (1 -(z[0])/(z))^(- a)* sum((a[s])/(factorial(s))* hypergeom([- s, b], [c], (1)/(z[0]))/GAMMA(c)*(1 -(z)/(z[0]))^(- s), s = 0..infinity)	Hypergeometric2F1Regularized[a, b, c, Divide[1,z]] == (1 -Divide[Subscript[z, 0],z])^(- a)* Sum[Divide[Subscript[a, s],(s)!]* Hypergeometric2F1Regularized[- s, b, c, Divide[1,Subscript[z, 0]]]*(1 -Divide[z,Subscript[z, 0]])^(- s), {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
15.16.E1	${\displaystyle{\displaystyle F\left({a,b\atop c-\frac{1}{2}};z\right)F\left({c-a,c-b\atop c+\frac{1}{2}};z\right)=\sum_{s=0}^{\infty}\frac{{\left(c\right)_{s}}}{{\left(c+\frac{1}{2}\right)_{s}}}A_{s}z^{s}}}$ \hyperF@@{a}{b}{c-\frac{1}{2}}{z}\hyperF@@{c-a}{c-b}{c+\frac{1}{2}}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{c}{s}}{\Pochhammersym{c+\frac{1}{2}}{s}}A_{s}z^{s}	${\displaystyle{\displaystyle|z|<1}}$	hypergeom([a, b], [c -(1)/(2)], z)*hypergeom([c - a, c - b], [c +(1)/(2)], z) = sum((pochhammer(c, s))/(pochhammer(c +(1)/(2), s))*A[s]*(z)^(s), s = 0..infinity)	Hypergeometric2F1[a, b, c -Divide[1,2], z]*Hypergeometric2F1[c - a, c - b, c +Divide[1,2], z] == Sum[Divide[Pochhammer[c, s],Pochhammer[c +Divide[1,2], s]]*Subscript[A, s]*(z)^(s), {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
15.16.E2	${\displaystyle{\displaystyle(1-z)^{a+b-c}F\left(2a,2b;2c-1;z\right)=\sum_{s=0}^{\infty}A_{s}z^{s}}}$ (1-z)^{a+b-c}\hyperF@{2a}{2b}{2c-1}{z} = \sum_{s=0}^{\infty}A_{s}z^{s}	${\displaystyle{\displaystyle|z|<1}}$	(1 - z)^(a + b - c)* hypergeom([2*a, 2*b], [2*c - 1], z) = sum(A[s]*(z)^(s), s = 0..infinity)	(1 - z)^(a + b - c)* Hypergeometric2F1[2*a, 2*b, 2*c - 1, z] == Sum[Subscript[A, s]*(z)^(s), {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: -1.113332374-1.*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2, A[s] = 1/2*3^(1/2)+1/2*I} Result: 1.618718434-1.732050808*I Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2, A[s] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.20011980854170835, -0.8439394617218601] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[A, s], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.3278316576066613, -0.6694818315348507] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[A, s], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.16.E3	${\displaystyle{\displaystyle F\left({a,b\atop c};z\right)F\left({a,b\atop c};\zeta\right)=\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}{\left(b\right)_{s}}{\left(c-a\right)_{s}}{\left(c-b\right)_{s}}}{{\left(c\right)_{s}}{\left(c\right)_{2s}}s!}\left(z\zeta\right)^{s}F\left({a+s,b+s\atop c+2s};z+\zeta-z\zeta\right)}}$ \hyperF@@{a}{b}{c}{z}\hyperF@@{a}{b}{c}{\zeta} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}\Pochhammersym{b}{s}\Pochhammersym{c-a}{s}\Pochhammersym{c-b}{s}}{\Pochhammersym{c}{s}\Pochhammersym{c}{2s}s!}\left(z\zeta\right)^{s}\hyperF@@{a+s}{b+s}{c+2s}{z+\zeta-z\zeta}	${\displaystyle{\displaystyle|z|<1,|\zeta|<1,|z+\zeta-z\zeta|<1}}$	hypergeom([a, b], [c], z)*hypergeom([a, b], [c], zeta) = sum((pochhammer(a, s)*pochhammer(b, s)*pochhammer(c - a, s)*pochhammer(c - b, s))/(pochhammer(c, s)*pochhammer(c, 2*s)*factorial(s))*(z*zeta)^(s)* hypergeom([a + s, b + s], [c + 2*s], z + zeta - z*zeta), s = 0..infinity)	Hypergeometric2F1[a, b, c, z]*Hypergeometric2F1[a, b, c, \[Zeta]] == Sum[Divide[Pochhammer[a, s]*Pochhammer[b, s]*Pochhammer[c - a, s]*Pochhammer[c - b, s],Pochhammer[c, s]*Pochhammer[c, 2*s]*(s)!]*(z*\[Zeta])^(s)* Hypergeometric2F1[a + s, b + s, c + 2*s, z + \[Zeta]- z*\[Zeta]], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
15.16.E4	${\displaystyle{\displaystyle F\left({a,b\atop c};z\right)F\left({-a,-b\atop-c};z\right)+\frac{ab(a-c)(b-c)}{c^{2}(1-c^{2})}z^{2}F\left({1+a,1+b\atop 2+c};z\right)F\left({1-a,1-b\atop 2-c};z\right)=1}}$ \hyperF@@{a}{b}{c}{z}\hyperF@@{-a}{-b}{-c}{z}+\frac{ab(a-c)(b-c)}{c^{2}(1-c^{2})}z^{2}\hyperF@@{1+a}{1+b}{2+c}{z}\hyperF@@{1-a}{1-b}{2-c}{z} = 1		hypergeom([a, b], [c], z)*hypergeom([- a, - b], [- c], z)+(a*b*(a - c)*(b - c))/((c)^(2)*(1 - (c)^(2)))*(z)^(2)* hypergeom([1 + a, 1 + b], [2 + c], z)*hypergeom([1 - a, 1 - b], [2 - c], z) = 1	Hypergeometric2F1[a, b, c, z]*Hypergeometric2F1[- a, - b, - c, z]+Divide[a*b*(a - c)*(b - c),(c)^(2)*(1 - (c)^(2))]*(z)^(2)* Hypergeometric2F1[1 + a, 1 + b, 2 + c, z]*Hypergeometric2F1[1 - a, 1 - b, 2 - c, z] == 1	Failure	Failure	Skipped - Because timed out	Failed [98 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
15.16.E5	${\displaystyle{\displaystyle F\left({\frac{1}{2}+\lambda,-\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)+F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({-\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)-F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)=\frac{\Gamma\left(1+\lambda+\mu\right)\Gamma\left(1+\nu+\mu\right)}{\Gamma\left(\lambda+\mu+\nu+\frac{3}{2}\right)\Gamma\left(\frac{1}{2}+\nu\right)}}}$ \hyperF@@{\frac{1}{2}+\lambda}{-\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z}+\hyperF@@{\frac{1}{2}+\lambda}{\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{-\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z}-\hyperF@@{\frac{1}{2}+\lambda}{\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z} = \frac{\EulerGamma@{1+\lambda+\mu}\EulerGamma@{1+\nu+\mu}}{\EulerGamma@{\lambda+\mu+\nu+\frac{3}{2}}\EulerGamma@{\frac{1}{2}+\nu}}	${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi,|\operatorname{ph}\left(1-z\right)|<\pi,\Re(1+\lambda+\mu)>0,\Re(1+\nu+\mu)>0,\Re(\lambda+\mu+\nu+\frac{3}{2})>0,\Re(\frac{1}{2}+\nu)>0}}$	hypergeom([(1)/(2)+ lambda, -(1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z)+ hypergeom([(1)/(2)+ lambda, (1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([-(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z)- hypergeom([(1)/(2)+ lambda, (1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z) = (GAMMA(1 + lambda + mu)*GAMMA(1 + nu + mu))/(GAMMA(lambda + mu + nu +(3)/(2))*GAMMA((1)/(2)+ nu))	Hypergeometric2F1[Divide[1,2]+ \[Lambda], -Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z]+ Hypergeometric2F1[Divide[1,2]+ \[Lambda], Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[-Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z]- Hypergeometric2F1[Divide[1,2]+ \[Lambda], Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z] == Divide[Gamma[1 + \[Lambda]+ \[Mu]]*Gamma[1 + \[Nu]+ \[Mu]],Gamma[\[Lambda]+ \[Mu]+ \[Nu]+Divide[3,2]]*Gamma[Divide[1,2]+ \[Nu]]]	Failure	Failure	Skipped - Because timed out	Failed [251 / 300] Result: Complex[0.3564253165633178, -0.5060695815565636] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ν, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} Result: Complex[0.011198613289511883, 0.30916385360889426] Test Values: {Rule[z, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ν, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]]} ... skip entries to safe data