8.15: 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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! 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/8.15.E1 8.15.E1] | | | [https://dlmf.nist.gov/8.15.E1 8.15.E1] || <math qid="Q2640">\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a+k)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, lambda*x) = (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, \[Lambda]*x] == \[Lambda]^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I | ||
Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I | Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I | ||
Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out | Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out | ||
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Latest revision as of 11:18, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 8.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}}
\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{a} > 0, \realpart@@{(a+k)} > 0} | GAMMA(a)-GAMMA(a, lambda*x) = (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)
|
Gamma[a, 0, \[Lambda]*x] == \[Lambda]^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]
|
Failure | Failure | Failed [90 / 90] Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = 1.5}
Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = .5}
... skip entries to safe data |
Skipped - Because timed out |