26.10: 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/26.10.E2 26.10.E2] | | | [https://dlmf.nist.gov/26.10.E2 26.10.E2] || <math qid="Q7885">\prod_{j=1}^{\infty}(1+q^{j}) = \prod_{j=1}^{\infty}\frac{1}{1-q^{2j-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\prod_{j=1}^{\infty}(1+q^{j}) = \prod_{j=1}^{\infty}\frac{1}{1-q^{2j-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>product(1 + (q)^(j), j = 1..infinity) = product((1)/(1 - (q)^(2*j - 1)), j = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Product[1 + (q)^(j), {j, 1, Infinity}, GenerateConditions->None] == Product[Divide[1,1 - (q)^(2*j - 1)], {j, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[] | ||
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br></div></div> | Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br></div></div> | ||
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| [https://dlmf.nist.gov/26.10.E3 26.10.E3] | | | [https://dlmf.nist.gov/26.10.E3 26.10.E3] || <math qid="Q7886">\sum_{m=0}^{k}\qbinom{k}{m}{q}q^{m(m+1)/2}x^{m} = \prod_{j=1}^{k}(1+x\,q^{j})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{m=0}^{k}\qbinom{k}{m}{q}q^{m(m+1)/2}x^{m} = \prod_{j=1}^{k}(1+x\,q^{j})</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>sum(QBinomial(k, m, q)*(q)^(m*(m + 1)/2)* (x)^(m), m = 0..k) = product(1 + x*(q)^(j), j = 1..k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[QBinomial[k,m,q]*(q)^(m*(m + 1)/2)* (x)^(m), {m, 0, k}, GenerateConditions->None] == Product[1 + x*(q)^(j), {j, 1, k}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 30] | ||
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</div> | </div> | ||
Latest revision as of 12:06, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 26.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \prod_{j=1}^{\infty}(1+q^{j}) = \prod_{j=1}^{\infty}\frac{1}{1-q^{2j-1}}}
\prod_{j=1}^{\infty}(1+q^{j}) = \prod_{j=1}^{\infty}\frac{1}{1-q^{2j-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | product(1 + (q)^(j), j = 1..infinity) = product((1)/(1 - (q)^(2*j - 1)), j = 1..infinity)
|
Product[1 + (q)^(j), {j, 1, Infinity}, GenerateConditions->None] == Product[Divide[1,1 - (q)^(2*j - 1)], {j, 1, Infinity}, GenerateConditions->None]
|
Failure | Failure | Error | Failed [1 / 10]
Result: DirectedInfinity[]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
|
| 26.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{m=0}^{k}\qbinom{k}{m}{q}q^{m(m+1)/2}x^{m} = \prod_{j=1}^{k}(1+x\,q^{j})}
\sum_{m=0}^{k}\qbinom{k}{m}{q}q^{m(m+1)/2}x^{m} = \prod_{j=1}^{k}(1+x\,q^{j}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x| < 1} | sum(QBinomial(k, m, q)*(q)^(m*(m + 1)/2)* (x)^(m), m = 0..k) = product(1 + x*(q)^(j), j = 1..k)
|
Sum[QBinomial[k,m,q]*(q)^(m*(m + 1)/2)* (x)^(m), {m, 0, k}, GenerateConditions->None] == Product[1 + x*(q)^(j), {j, 1, k}, GenerateConditions->None]
|
Failure | Failure | Error | Successful [Tested: 30] |