8.22: 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/8.22.E1 8.22.E1] | | | [https://dlmf.nist.gov/8.22.E1 8.22.E1] || <math qid="Q2750">\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</syntaxhighlight> || <math>\realpart@@{p} > 0, \realpart@@{(n+p)} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z) = (GAMMA(p))/(2*Pi)*GAMMA(1 - p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z] == Divide[Gamma[p],2*Pi]*Gamma[1 - p, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 35] | ||
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| [https://dlmf.nist.gov/8.22.E3 8.22.E3] | | | [https://dlmf.nist.gov/8.22.E3 8.22.E3] || <math qid="Q2752">\zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}</syntaxhighlight> || <math>\realpart@@{s} > 1</math> || <syntaxhighlight lang=mathematica>((1)/(GAMMA(s))*int(((t)^(s - 1))/(exp(t)- 1), t = 0..x)) = sum((k)^(- s)* (GAMMA(s)-GAMMA(s, k*x))/GAMMA(s), k = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[1,Gamma[s]]*Integrate[Divide[(t)^(s - 1),Exp[t]- 1], {t, 0, x}, GenerateConditions->None]) == Sum[(k)^(- s)* GammaRegularized[s, 0, k*x], {k, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out | ||
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Latest revision as of 11:19, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 8.22.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}}
\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{p} > 0, \realpart@@{(n+p)} > 0} | (GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z) = (GAMMA(p))/(2*Pi)*GAMMA(1 - p, z)
|
Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z] == Divide[Gamma[p],2*Pi]*Gamma[1 - p, z]
|
Successful | Successful | - | Successful [Tested: 35] |
| 8.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}}
\zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{s} > 1} | ((1)/(GAMMA(s))*int(((t)^(s - 1))/(exp(t)- 1), t = 0..x)) = sum((k)^(- s)* (GAMMA(s)-GAMMA(s, k*x))/GAMMA(s), k = 1..infinity)
|
(Divide[1,Gamma[s]]*Integrate[Divide[(t)^(s - 1),Exp[t]- 1], {t, 0, x}, GenerateConditions->None]) == Sum[(k)^(- s)* GammaRegularized[s, 0, k*x], {k, 1, Infinity}, GenerateConditions->None]
|
Failure | Aborted | Manual Skip! | Skipped - Because timed out |