Difference between revisions of "Q-shifted factorial"

From specialfunctionswiki
Jump to: navigation, search
(References)
Line 5: Line 5:
  
 
=References=
 
=References=
 +
* {{PaperReference|The q-gamma function for q greater than 1|1980|Daniel S. Moak|prev=Q-gamma|next=findme}}
 
* {{PaperReference|q-Special functions, a tutorial|1994|Tom H. Koornwinder|prev=findme|next=findme}}  
 
* {{PaperReference|q-Special functions, a tutorial|1994|Tom H. Koornwinder|prev=findme|next=findme}}  
 
* {{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")
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 00:14, 30 May 2017

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