Q-shifted factorial

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The $q$-shifted factorial $(a;q)_n$ is defined for $a,q \in \mathbb{C}$ by $(a;q)_0=1$ and for $n=1,2,3,\ldots$ or $n=\infty$, by $$(a;q)_n=\displaystyle\prod_{k=0}^{n-1} 1-aq^{k}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$

Properties

References