q-Pochhammer symbol

Summary

The $q$-Pochhammer symbol $(a; q)_n = (1 - a)(1 - aq) \cdots (1 - aq^{n-1})$ is a $q$-analogue of the rising factorial. Its infinite version $(a; q)_\infty$ is a convergent infinite product for $\abs{q} < 1$. It is the basic building block of $q$-series, basic hypergeometric series and generating functions for integer partitions. The exact definition is in q-Pochhammer symbol.