15.15: 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/15.15.E1 15.15.E1] | | | [https://dlmf.nist.gov/15.15.E1 15.15.E1] || <math qid="Q5177">\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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out | ||
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Latest revision as of 11:41, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 15.15.E1 | \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} |
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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)
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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]
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Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |