Difference between revisions of "Q-factorial"
From specialfunctionswiki
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The $q$-factorial is defined for a non-negative integer $k$ by | The $q$-factorial is defined for a non-negative integer $k$ by | ||
| − | $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q= | + | $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q= \left( \dfrac{1-q}{1-q} \right) \left( \dfrac{1-q^2}{1-q} \right) \ldots \left( \dfrac{1-q^n}{1-q} \right),$$ |
where $[k]_q$ denotes a [[q-number|$q$-number]]. | where $[k]_q$ denotes a [[q-number|$q$-number]]. | ||
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=See Also= | =See Also= | ||
[[q-number|$q$-number]]<br /> | [[q-number|$q$-number]]<br /> | ||
| + | [[q-Pochhammer|$q$-Pochhammer]]<br /> | ||
=References= | =References= | ||
Revision as of 21:10, 18 December 2016
The $q$-factorial is defined for a non-negative integer $k$ by $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q= \left( \dfrac{1-q}{1-q} \right) \left( \dfrac{1-q^2}{1-q} \right) \ldots \left( \dfrac{1-q^n}{1-q} \right),$$ 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): ($6.3$)
