15.14: 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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| [https://dlmf.nist.gov/15.14.E1 15.14.E1] | | | [https://dlmf.nist.gov/15.14.E1 15.14.E1] || <math qid="Q5176">\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}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <math>\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</math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out | ||
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Latest revision as of 12:41, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 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))
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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]]
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Successful | Aborted | - | Skipped - Because timed out |