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

$q$-number

References

$q$-calculus