Difference between revisions of "Q-shifted factorial"
From specialfunctionswiki
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The $q$-shifted factorial $(a;q)_n$ is defined by the formula | The $q$-shifted factorial $(a;q)_n$ is defined by the formula | ||
$$(a;q)_n=\displaystyle\prod_{k=0}^{n-1} 1-aq^{k-1}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$ | $$(a;q)_n=\displaystyle\prod_{k=0}^{n-1} 1-aq^{k-1}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$ | ||
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| + | =Properties= | ||
=References= | =References= | ||
| − | * {{BookReference|Special Functions|1999|George E. Andrews|author2=Richard Askey|author3=Ranjan Roy|prev=findme|next=findme}} $(10.2.1)$ | + | * {{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") |
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 20:57, 18 December 2016
The $q$-shifted factorial $(a;q)_n$ is defined by the formula $$(a;q)_n=\displaystyle\prod_{k=0}^{n-1} 1-aq^{k-1}=(1-a)(1-aq)(1-aq^2)\ldots(1-aq^{n-1}).$$
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")
