17.8: Difference between revisions

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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/17.8.E1 17.8.E1] || [[Item:Q5420|<math>\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- z)^(n)* (q)^(n*(n - 1)/2), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , z , q/z},i],q,Infinity],{i,1,Length[{q , z , q/z}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
| [https://dlmf.nist.gov/17.8.E1 17.8.E1] || <math qid="Q5420">\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- z)^(n)* (q)^(n*(n - 1)/2), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , z , q/z},i],q,Infinity],{i,1,Length[{q , z , q/z}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/17.8.E3 17.8.E3] || [[Item:Q5422|<math>\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (z)^(3*n)*(1 + z*(q)^(n)), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , - z , - q/z},i],q,Infinity],{i,1,Length[{q , - z , - q/z}]}]*Product[QPochhammer[Part[{q*(z)^(2), q/(z)^(2)},i],(q)^(2),Infinity],{i,1,Length[{q*(z)^(2), q/(z)^(2)}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
| [https://dlmf.nist.gov/17.8.E3 17.8.E3] || <math qid="Q5422">\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (z)^(3*n)*(1 + z*(q)^(n)), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , - z , - q/z},i],q,Infinity],{i,1,Length[{q , - z , - q/z}]}]*Product[QPochhammer[Part[{q*(z)^(2), q/(z)^(2)},i],(q)^(2),Infinity],{i,1,Length[{q*(z)^(2), q/(z)^(2)}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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Latest revision as of 11:43, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
17.8.E1 ∑ n = - ∞ ∞ ( - z ) n ⁢ q n ⁢ ( n - 1 ) / 2 = ( q , z , q / z ; q ) ∞ superscript subscript 𝑛 superscript 𝑧 𝑛 superscript 𝑞 𝑛 𝑛 1 2 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2}=% \left(q,z,q/z;q\right)_{\infty}}}
\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}		 

Error

Sum[(- z)^(n)* (q)^(n*(n - 1)/2), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , z , q/z},i],q,Infinity],{i,1,Length[{q , z , q/z}]}]
Missing Macro Error Aborted - Skipped - Because timed out
17.8.E3 ∑ n = - ∞ ∞ ( - 1 ) n ⁢ q n ⁢ ( 3 ⁢ n - 1 ) / 2 ⁢ z 3 ⁢ n ⁢ ( 1 + z ⁢ q n ) = ( q , - z , - q / z ; q ) ∞ ⁢ ( q ⁢ z 2 , q / z 2 ; q 2 ) ∞ superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑞 𝑛 3 𝑛 1 2 superscript 𝑧 3 𝑛 1 𝑧 superscript 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 q-multiple-Pochhammer 𝑞 superscript 𝑧 2 𝑞 superscript 𝑧 2 superscript 𝑞 2 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3% n}(1+zq^{n})=\left(q,-z,-q/z;q\right)_{\infty}\left(qz^{2},q/{z^{2}};q^{2}% \right)_{\infty}}}
\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}		 

Error

Sum[(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (z)^(3*n)*(1 + z*(q)^(n)), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , - z , - q/z},i],q,Infinity],{i,1,Length[{q , - z , - q/z}]}]*Product[QPochhammer[Part[{q*(z)^(2), q/(z)^(2)},i],(q)^(2),Infinity],{i,1,Length[{q*(z)^(2), q/(z)^(2)}]}]
Missing Macro Error Aborted - Skipped - Because timed out
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