q -Hypergeometric and Related Functions - 17.8 Special Cases of Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
17.8.E1	${\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2}=\left(q,z,q/z;q\right)_{\infty}}}$ \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	${\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n})=\left(q,-z,-q/z;q\right)_{\infty}\left(qz^{2},q/{z^{2}};q^{2}\right)_{\infty}}}$ \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