Q-shifted factorial
From specialfunctionswiki
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
- Daniel S. Moak: The q-gamma function for q greater than 1 (1980)... (previous)... (next)
- Tom H. Koornwinder: q-Special functions, a tutorial (1994)... (previous)... (next)
- 1999: George E. Andrews, Richard Askey and Ranjan Roy: Special Functions ... (previous) ... (next) $(10.2.1)$ (does not specifically say "$q$-shifted factorial")
