= q-series
A <q-series> is a series in a parameter $q$, treated either as a <formal power series> or as an analytic series, often for $|q|<1$. Its coefficients can encode a <sequence>, while identities involving infinite products record choices of parts in <integer partitions>.
For example,
$$
\prod_{m\ge1}(1-q^m)^{-1}=\sum_{n\ge0}p(n)q^n,
$$
where $p(n)$ counts <integer partitions> of $n$. Expanding each factor as a <geometric series> chooses the number of parts of size $m$. Formally, each coefficient uses only finitely many factors. This product is a basic link between <combinatorics>, <number theory>, and <modular forms>.
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