# DLMF:17.14.E3 (Q5472)

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DLMF:17.14.E3
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## Statements

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{q^{n(n+1)}}{\left(q^{2};q% ^{2}\right)_{n}\left(-q;q^{2}\right)_{n+1}}=\mbox{ coeff. of }z^{0}\mbox{ in }% \frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left% (q^{2};q^{2}\right)_{\infty}}{\left(z^{-1};q^{2}\right)_{\infty}\left(-q;q^{2}% \right)_{\infty}\left(z^{-1}q;q^{2}\right)_{\infty}}=\frac{1}{\left(-q;q^{2}% \right)_{\infty}}\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right% )_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty% }}{\left(z^{-1};q\right)_{\infty}}=\frac{G(q)}{\left(-q;q^{2}\right)_{\infty}}% ,}}$
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DLMF:17.14.E3
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${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$
C17.S2.SS1.p1.m2abdec
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${\displaystyle{\displaystyle q}}$
C17.S1.XMD10.m1bdec
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${\displaystyle{\displaystyle n}}$
C17.S1.XMD4.m1bdec
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${\displaystyle{\displaystyle z}}$
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${\displaystyle{\displaystyle G(q)}}$
C17.S14.XMD1.m1dec
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