27.7: 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/27.7.E4 27.7.E4] | | | [https://dlmf.nist.gov/27.7.E4 27.7.E4] || <math qid="Q8044">\sum_{n=1}^{\infty}\Eulertotientphi[]@{n}\frac{x^{n}}{1-x^{n}} = \frac{x}{(1-x)^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}\Eulertotientphi[]@{n}\frac{x^{n}}{1-x^{n}} = \frac{x}{(1-x)^{2}}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>sum(phi(n)*((x)^(n))/(1 - (x)^(n)), n = 1..infinity) = (x)/((1 - x)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[EulerPhi[n]*Divide[(x)^(n),1 - (x)^(n)], {n, 1, Infinity}, GenerateConditions->None] == Divide[x,(1 - x)^(2)]</syntaxhighlight> || Failure || Successful || Successful [Tested: 1] || Successful [Tested: 1] | ||
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| [https://dlmf.nist.gov/27.7.E5 27.7.E5] | | | [https://dlmf.nist.gov/27.7.E5 27.7.E5] || <math qid="Q8045">\sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}} = \sum_{n=1}^{\infty}\sumdivisors{\alpha}@{n}x^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}} = \sum_{n=1}^{\infty}\sumdivisors{\alpha}@{n}x^{n}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>sum((n)^(alpha)*((x)^(n))/(1 - (x)^(n)), n = 1..infinity) = sum(add(divisors(alpha))*(x)^(n), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.671514971 | ||
Test Values: {alpha = 3/2, x = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.507450946 | Test Values: {alpha = 3/2, x = 1/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.507450946 | ||
Test Values: {alpha = 1/2, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || - | Test Values: {alpha = 1/2, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || - | ||
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Latest revision as of 12:06, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 27.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}\Eulertotientphi[]@{n}\frac{x^{n}}{1-x^{n}} = \frac{x}{(1-x)^{2}}}
\sum_{n=1}^{\infty}\Eulertotientphi[]@{n}\frac{x^{n}}{1-x^{n}} = \frac{x}{(1-x)^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x| < 1} | sum(phi(n)*((x)^(n))/(1 - (x)^(n)), n = 1..infinity) = (x)/((1 - x)^(2))
|
Sum[EulerPhi[n]*Divide[(x)^(n),1 - (x)^(n)], {n, 1, Infinity}, GenerateConditions->None] == Divide[x,(1 - x)^(2)]
|
Failure | Successful | Successful [Tested: 1] | Successful [Tested: 1] |
| 27.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}} = \sum_{n=1}^{\infty}\sumdivisors{\alpha}@{n}x^{n}}
\sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}} = \sum_{n=1}^{\infty}\sumdivisors{\alpha}@{n}x^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x| < 1} | sum((n)^(alpha)*((x)^(n))/(1 - (x)^(n)), n = 1..infinity) = sum(add(divisors(alpha))*(x)^(n), n = 1..infinity)
|
Error
|
Failure | Missing Macro Error | Failed [3 / 3] Result: 2.671514971
Test Values: {alpha = 3/2, x = 1/2}
Result: 1.507450946
Test Values: {alpha = 1/2, x = 1/2}
... skip entries to safe data |
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