15.1: Difference between revisions
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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ||
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| [https://dlmf.nist.gov/15.1.E1 15.1.E1] | | | [https://dlmf.nist.gov/15.1.E1 15.1.E1] || <math qid="Q4975">\genhyperF{2}{1}@{a,b}{c}{z} = \hyperF@{a}{b}{c}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genhyperF{2}{1}@{a,b}{c}{z} = \hyperF@{a}{b}{c}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>hypergeom([a , b], [c], z) = hypergeom([a, b], [c], z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>HypergeometricPFQ[{a , b}, {c}, z] == Hypergeometric2F1[a, b, c, z]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
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| [https://dlmf.nist.gov/15.1.E1 15.1.E1] | | | [https://dlmf.nist.gov/15.1.E1 15.1.E1] || <math qid="Q4975">\hyperF@{a}{b}{c}{z} = \hyperF@@{a}{b}{c}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\hyperF@{a}{b}{c}{z} = \hyperF@@{a}{b}{c}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>hypergeom([a, b], [c], z) = hypergeom([a, b], [c], z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Hypergeometric2F1[a, b, c, z] == Hypergeometric2F1[a, b, c, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300] | ||
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| [https://dlmf.nist.gov/15.1.E2 15.1.E2] | | | [https://dlmf.nist.gov/15.1.E2 15.1.E2] || <math qid="Q4976">\frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{c}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{c}{z}</syntaxhighlight> || <math>\realpart@@{c} > 0, |z| < 1</math> || <syntaxhighlight lang=mathematica>(hypergeom([a, b], [c], z))/(GAMMA(c)) = hypergeom([a, b], [c], z)/GAMMA(c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Hypergeometric2F1[a, b, c, z],Gamma[c]] == Hypergeometric2F1Regularized[a, b, c, z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 108] | ||
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| [https://dlmf.nist.gov/15.1.E2 15.1.E2] | | | [https://dlmf.nist.gov/15.1.E2 15.1.E2] || <math qid="Q4976">\hyperOlverF@{a}{b}{c}{z} = \hyperOlverF@@{a}{b}{c}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\hyperOlverF@{a}{b}{c}{z} = \hyperOlverF@@{a}{b}{c}{z}</syntaxhighlight> || <math>\realpart@@{c} > 0, |z| < 1</math> || <syntaxhighlight lang=mathematica>hypergeom([a, b], [c], z)/GAMMA(c) = hypergeom([a, b], [c], z)/GAMMA(c)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Hypergeometric2F1Regularized[a, b, c, z] == Hypergeometric2F1Regularized[a, b, c, z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 108] | ||
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| [https://dlmf.nist.gov/15.1.E2 15.1.E2] | | | [https://dlmf.nist.gov/15.1.E2 15.1.E2] || <math qid="Q4976">\hyperOlverF@@{a}{b}{c}{z} = \genhyperOlverF{2}{1}@{a,b}{c}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\hyperOlverF@@{a}{b}{c}{z} = \genhyperOlverF{2}{1}@{a,b}{c}{z}</syntaxhighlight> || <math>\realpart@@{c} > 0, |z| < 1</math> || <syntaxhighlight lang=mathematica>hypergeom([a, b], [c], z)/GAMMA(c) = hypergeom([a , b], [c], z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Hypergeometric2F1Regularized[a, b, c, z] == HypergeometricPFQRegularized[{a , b}, {c}, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [175 / 216]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2039500354 | ||
Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .227101342 | Test Values: {a = -3/2, b = -3/2, c = -3/2, z = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .227101342 | ||
Test Values: {a = -3/2, b = -3/2, c = 3/2, z = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 108] | Test Values: {a = -3/2, b = -3/2, c = 3/2, z = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 108] | ||
|} | |} | ||
</div> | </div> | ||
Latest revision as of 11:38, 28 June 2021
| 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)
|
HypergeometricPFQ[{a , b}, {c}, z] == Hypergeometric2F1[a, b, c, z]
|
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)
|
Divide[Hypergeometric2F1[a, b, c, z],Gamma[c]] == Hypergeometric2F1Regularized[a, b, c, z]
|
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)
|
Hypergeometric2F1Regularized[a, b, c, z] == Hypergeometric2F1Regularized[a, b, c, z]
|
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)
|
Hypergeometric2F1Regularized[a, b, c, z] == HypergeometricPFQRegularized[{a , b}, {c}, z]
|
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] |