17.3: 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/17.3.E1 17.3.E1] | | | [https://dlmf.nist.gov/17.3.E1 17.3.E1] || <math qid="Q5341">\sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)*x, q, infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)*x, q, Infinity]]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out | ||
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| [https://dlmf.nist.gov/17.3.E2 17.3.E2] | | | [https://dlmf.nist.gov/17.3.E2 17.3.E2] || <math qid="Q5342">\sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)*x, q, infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(1 - q)^(n)* (q)^(Binomial[n,2])* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[-(1 - q)*x, q, Infinity]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out | ||
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Latest revision as of 12:42, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 17.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}}
\sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)*x, q, infinity))
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Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)*x, q, Infinity]]
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Failure | Aborted | Error | Skipped - Because timed out |
| 17.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}}
\sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)*x, q, infinity)
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Sum[Divide[(1 - q)^(n)* (q)^(Binomial[n,2])* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[-(1 - q)*x, q, Infinity]
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Failure | Aborted | Error | Skipped - Because timed out |