Difference between revisions of "Q-factorial"
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Revision as of 03:00, 21 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
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): ($6.3$)
