Difference between revisions of "Q-factorial"
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=References= | =References= | ||
* {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=Q-exponential E sub q|next=findme}} | * {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=Q-exponential E sub q|next=findme}} | ||
| + | * {{BookReference|Special Functions|1999|George E. Andrews|author2=Richard Askey|author3=Ranjan Roy|prev=q-number|next=findme}} | ||
* {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=Q-number when a=n is a natural number|next=findme}}: ($6.3$) | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=Q-number when a=n is a natural number|next=findme}}: ($6.3$) | ||
Revision as of 20:53, 18 December 2016
The $q$-factorial is defined for a non-negative integer $k$ by $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q=[1]_q [2]_q \ldots [n]_q,$$ where $[k]_q$ denotes a $q$-number.
Properties
Q-derivative power rule
Relationship between q-factorial and q-pochhammer
See Also
References
- D.S. McAnally: q-exponential and q-gamma functions. I. q-exponential functions (1994)... (previous)... (next)
- 1999: George E. Andrews, Richard Askey and Ranjan Roy: Special Functions ... (previous) ... (next)
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.3$)
