Results of Hypergeometric Function II
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 15.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)\deriv[2]{w}{z}+\left(c-(a+b+1)z\right)\deriv{w}{z}-abw = 0}
z(1-z)\deriv[2]{w}{z}+\left(c-(a+b+1)z\right)\deriv{w}{z}-abw = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = \hyperF@@{a}{b}{c}{z}}
f_{1}(z) = \hyperF@@{a}{b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z) = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}}
f_{2}(z) = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{2-c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{f_{1}(z),f_{2}(z)} = (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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = \hyperF@@{a}{b}{a+b+1-c}{1-z}}
f_{1}(z) = \hyperF@@{a}{b}{a+b+1-c}{1-z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{f_{1}(z),f_{2}(z)} = (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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = z^{-a}\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}}
f_{1}(z) = z^{-a}\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z) = z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}}
f_{2}(z) = z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{f_{1}(z),f_{2}(z)} = (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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = \hyperF@@{a}{b}{c}{z}}
w_{1}(z) = \hyperF@@{a}{b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{c}{z} = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z}}
\hyperF@@{a}{b}{c}{z} = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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}\hyperF@@{c-a}{c-b}{c}{z} = (1-z)^{-a}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}} = (1-z)^{-b}\hyperF@@{c-a}{b}{c}{\frac{z}{z-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}}
w_{2}(z) = {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {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}}\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {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}}\*\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {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}}\*\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{3}(z) = \hyperF@@{a}{b}{a+b-c+1}{1-z}}
w_{3}(z) = \hyperF@@{a}{b}{a+b-c+1}{1-z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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}\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{5}(z) = e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}}
w_{5}(z) = e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}}}
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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}}}
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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{6}(z) = e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}}
w_{6}(z) = e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}}}
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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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}}}
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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (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}\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1-c)} > 0, \realpart@@{(a+b-c+1)} > 0, \realpart@@{(a-c+1)} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(c-1)} > 0, \realpart@@{a} > 0, \realpart@@{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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1-c)} > 0, \realpart@@{(c-a-b+1)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(c-1)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1-c)} > 0, \realpart@@{(a-b+1)} > 0, \realpart@@{(a-c+1)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(c-1)} > 0, \realpart@@{a} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1-c)} > 0, \realpart@@{(b-a+1)} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(c-1)} > 0, \realpart@@{b} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(c-a-b)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(c-b)} > 0, \realpart@@{(a+b-c)} > 0, \realpart@@{a} > 0, \realpart@@{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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{(c-a-b)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(a+b-c)} > 0, \realpart@@{(a-c+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(a-b+1)} > 0, \realpart@@{(c-a-b)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(c-b)} > 0, \realpart@@{(a+b-c)} > 0, \realpart@@{a} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(b-a+1)} > 0, \realpart@@{(c-a-b)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(a+b-c)} > 0, \realpart@@{b} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(b-a)} > 0, \realpart@@{b} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(a-b)} > 0, \realpart@@{a} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{(b-a)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(a-b)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(a+b-c+1)} > 0, \realpart@@{(b-a)} > 0, \realpart@@{b} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(a-b)} > 0, \realpart@@{a} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(c-a-b+1)} > 0, \realpart@@{(b-a)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(a-b)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(a-c+1)} > 0, \realpart@@{(a+b-c+1)} > 0, \realpart@@{(c-b)} > 0, \realpart@@{b} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(a+b-c+1)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{a} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{a} > 0, \realpart@@{(a+b-c+1)} > 0, \realpart@@{(1-b)} > 0, \realpart@@{(a-b+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{b} > 0, \realpart@@{(a+b-c+1)} > 0, \realpart@@{(1-a)} > 0, \realpart@@{(b-a+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(1-b)} > 0, \realpart@@{a} > 0, \realpart@@{(c-a-b+1)} > 0, \realpart@@{(a-b+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, \realpart@@{(1-a)} > 0, \realpart@@{b} > 0, \realpart@@{(c-a-b+1)} > 0, \realpart@@{(b-a+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{(c-b)} > 0, \realpart@@{(a-c+1)} > 0, \realpart@@{(c-a-b+1)} > 0, \realpart@@{(a-b+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 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)}
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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(2-c)} > 0, \realpart@@{(c-a)} > 0, \realpart@@{(b-c+1)} > 0, \realpart@@{(c-a-b+1)} > 0, \realpart@@{(b-a+1)} > 0, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t = \ifrac{(\kappa z+\lambda)}{(\mu z+\nu)}}
t = \ifrac{(\kappa z+\lambda)}{(\mu z+\nu)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{+} = \atan@{\frac{\phase@@{z}-\phase@{1-z}-\pi}{\ln@@{|1-z^{-1}|}}}}
\alpha_{+} = \atan@{\frac{\phase@@{z}-\phase@{1-z}-\pi}{\ln@@{|1-z^{-1}|}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{-} = \atan@{\frac{\phase@@{z}-\phase@{1-z}+\pi}{\ln@@{|1-z^{-1}|}}}}
\alpha_{-} = \atan@{\frac{\phase@@{z}-\phase@{1-z}+\pi}{\ln@@{|1-z^{-1}|}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | ((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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \acosh@@{z}}
\zeta = \acosh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \left(-2\ln@{1-\left(\frac{z-1}{z+1}\right)^{2}}\right)^{1/2}}
\alpha = \left(-2\ln@{1-\left(\frac{z-1}{z+1}\right)^{2}}\right)^{1/2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \acosh@{\tfrac{1}{4}z-1}}
\zeta = \acosh@{\tfrac{1}{4}z-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \left(-\frac{3}{2}\zeta+\frac{9}{4}\ln@{\frac{2+e^{\zeta}}{2+e^{-\zeta}}}\right)^{1/3}}
\beta = \left(-\frac{3}{2}\zeta+\frac{9}{4}\ln@{\frac{2+e^{\zeta}}{2+e^{-\zeta}}}\right)^{1/3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}}
\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \min(\realpart@@{a} > \realpart@@{s}, \realpart@@{b}) > \realpart@@{s}, \realpart@@{s} > 0, \realpart@@{(a-s)} > 0, \realpart@@{(b-s)} > 0, \realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(c-s)} > 0, |(-x)| < 1, \realpart@@{(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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{a+b-c}\hyperF@{2a}{2b}{2c-1}{z} = \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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}
\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 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}}
\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}| < \pi, |\phase@{1-z}| < \pi, \realpart@@{(1+\lambda+\mu)} > 0, \realpart@@{(1+\nu+\mu)} > 0, \realpart@@{(\lambda+\mu+\nu+\frac{3}{2})} > 0, \realpart@@{(\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 |