Formula:6171

Digital Library of Mathematical Functions ID 17.14.E5

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{q^{n^{2}+2n}}{\left(q^{2};q^{2}\right)_{n}\left(q;q^{2}\right)_{n+1}}=\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty}}{\left(-q^{2}z^{-1};q^{2}\right)_{\infty}\left(q;q^{2}\right)_{\infty}\left(z^{-1}q^{2};q^{2}\right)_{\infty}}=\frac{1}{\left(q;q^{2}\right)_{\infty}}\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty}}{\left(q^{4}z^{-2};q^{4}\right)_{\infty}}=\frac{H(q^{4})}{\left(q;q^{2}\right)_{\infty}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle H(q)}}$: LHS of ()
 

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