# DLMF:17.14.E4 (Q5473)

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DLMF:17.14.E4
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## Statements

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{q^{n^{2}}}{\left(q^{2};q^% {2}\right)_{n}\left(q;q^{2}\right)_{n}}=\mbox{ coeff. of }z^{0}\mbox{ in }% \frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left% (q^{2};q^{2}\right)_{\infty}}{\left(-z^{-1};q^{2}\right)_{\infty}\left(q;q^{2}% \right)_{\infty}\left(z^{-1};q^{2}\right)_{\infty}}=\frac{1}{\left(q;q^{2}% \right)_{\infty}}\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right% )_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty% }}{\left(z^{-2};q^{4}\right)_{\infty}}=\frac{G(q^{4})}{\left(q;q^{2}\right)_{% \infty}},}}$
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DLMF:17.14.E4
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${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$
C17.S2.SS1.p1.m2acdec
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${\displaystyle{\displaystyle q}}$
C17.S1.XMD10.m1cdec
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${\displaystyle{\displaystyle n}}$
C17.S1.XMD4.m1cdec
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${\displaystyle{\displaystyle z}}$
C17.S1.XMD7.m1bdec
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${\displaystyle{\displaystyle G(q)}}$