= Reciprocal geometric infinite product
{title2=$S_q(z)$}
For $|q|>1$, define $S_q(z)=\prod_{k\geq0}(1-q^{-2k-1}z)(1-q^{-2k-1}z^{-1})$ on $\mathbb C^*$. The geometric decay gives locally uniform absolute tail convergence there. Its <simple zeros> are $q^{2k+1}$ and $q^{-2k-1}$ for $k\geq0$, and reindexing gives $S_q(qz)=-zS_q(q^{-1}z)$. The variable zero is outside its domain, and the poles introduced by each reciprocal factor cannot be interpreted as a value of the product at zero.
// Destination: analysis.bigb
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