q -Hypergeometric and Related Functions - 17.8 Special Cases of Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 17.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}}
\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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}]}]
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Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 17.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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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)}]}]
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Missing Macro Error | Aborted | - | Skipped - Because timed out |