Hypergeometric Function - 15.10 Hypergeometric Differential Equation

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