Legendre and Related Functions - 15.1 Special Notation
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 15.1.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{2}{1}@{a,b}{c}{z} = \hyperF@{a}{b}{c}{z}}
\genhyperF{2}{1}@{a,b}{c}{z} = \hyperF@{a}{b}{c}{z} |
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)
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HypergeometricPFQ[{a , b}, {c}, z] == Hypergeometric2F1[a, b, c, z]
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Successful | Successful | - | Failed [42 / 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 |
| 15.1.E1 | 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}}
\hyperF@{a}{b}{c}{z} = \hyperF@@{a}{b}{c}{z} |
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)
|
Hypergeometric2F1[a, b, c, z] == Hypergeometric2F1[a, b, c, z]
|
Successful | Successful | - | Successful [Tested: 300] |
| 15.1.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{c}{z}}
\frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, |z| < 1} | (hypergeom([a, b], [c], z))/(GAMMA(c)) = hypergeom([a, b], [c], z)/GAMMA(c)
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Divide[Hypergeometric2F1[a, b, c, z],Gamma[c]] == Hypergeometric2F1Regularized[a, b, c, z]
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Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 108] |
| 15.1.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{a}{b}{c}{z} = \hyperOlverF@@{a}{b}{c}{z}}
\hyperOlverF@{a}{b}{c}{z} = \hyperOlverF@@{a}{b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, |z| < 1} | hypergeom([a, b], [c], z)/GAMMA(c) = hypergeom([a, b], [c], z)/GAMMA(c)
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Hypergeometric2F1Regularized[a, b, c, z] == Hypergeometric2F1Regularized[a, b, c, z]
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Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 108] |
| 15.1.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{c}{z} = \genhyperOlverF{2}{1}@{a,b}{c}{z}}
\hyperOlverF@@{a}{b}{c}{z} = \genhyperOlverF{2}{1}@{a,b}{c}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{c} > 0, |z| < 1} | hypergeom([a, b], [c], z)/GAMMA(c) = hypergeom([a , b], [c], z)
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Hypergeometric2F1Regularized[a, b, c, z] == HypergeometricPFQRegularized[{a , b}, {c}, z]
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Failure | Successful | Failed [175 / 216] Result: -.2039500354
Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2}
Result: .227101342
Test Values: {a = -3/2, b = -3/2, c = 3/2, z = 1/2}
... skip entries to safe data |
Successful [Tested: 108] |