Difference between revisions of "Q-shifted factorial"
From specialfunctionswiki
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| − | The $q$-shifted factorial $(a;q)_n$ is defined by | + | The $q$-shifted factorial $(a;q)_n$ is defined for $a,q \in \mathbb{C}$ by $(a;q)_0=1$ and for $n=1,2,3,\ldots$, by |
| − | + | $$\displaystyle\prod_{k=0}^{n-1} 1-aq^{k-1}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$ | |
=Properties= | =Properties= | ||
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=References= | =References= | ||
* {{BookReference|Special Functions|1999|George E. Andrews|author2=Richard Askey|author3=Ranjan Roy|prev=findme|next=findme}} $(10.2.1)$ (does not specifically say "$q$-shifted factorial") | * {{BookReference|Special Functions|1999|George E. Andrews|author2=Richard Askey|author3=Ranjan Roy|prev=findme|next=findme}} $(10.2.1)$ (does not specifically say "$q$-shifted factorial") | ||
| + | * {{PaperReference|q-Special functions, a tutorial|1994|Tom H. Koornwinder|prev=findme|next=findme}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 02:54, 21 December 2016
The $q$-shifted factorial $(a;q)_n$ is defined for $a,q \in \mathbb{C}$ by $(a;q)_0=1$ and for $n=1,2,3,\ldots$, by $$\displaystyle\prod_{k=0}^{n-1} 1-aq^{k-1}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$
Properties
References
- 1999: George E. Andrews, Richard Askey and Ranjan Roy: Special Functions ... (previous) ... (next) $(10.2.1)$ (does not specifically say "$q$-shifted factorial")
- Tom H. Koornwinder: q-Special functions, a tutorial (1994)... (previous)... (next)
