Difference between revisions of "Q-factorial"
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| − | The $q$- | + | The $q$-factorial is defined for a non-negative integer $k$ by |
$$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q=[1]_q [2]_q \ldots [n]_q,$$ | $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q=[1]_q [2]_q \ldots [n]_q,$$ | ||
where $[k]_q$ denotes a [[q-number|$q$-number]]. | where $[k]_q$ denotes a [[q-number|$q$-number]]. | ||
Revision as of 20:06, 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)
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.3$)
