# DLMF:17.14.E2 (Q5471)

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DLMF:17.14.E2
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## Statements

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{q^{n(n+1)}}{\left(q^{2};q% ^{2}\right)_{n}\left(-q;q^{2}\right)_{n+1}}=\mbox{ coeff. of }z^{0}\mbox{ in }% \frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left% (q^{2};q^{2}\right)_{\infty}}{\left(z^{-1}q^{2};q^{2}\right)_{\infty}\left(-q;% q^{2}\right)_{\infty}\left(z^{-1}q;q^{2}\right)_{\infty}}=\frac{1}{\left(-q;q^% {2}\right)_{\infty}}\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}% \right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{% \infty}}{\left(z^{-1}q;q\right)_{\infty}}=\frac{H(q)}{\left(-q;q^{2}\right)_{% \infty}},}}$
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DLMF:17.14.E2
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${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$
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${\displaystyle{\displaystyle q}}$
${\displaystyle{\displaystyle n}}$
${\displaystyle{\displaystyle z}}$
${\displaystyle{\displaystyle H(q)}}$