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 | ||
| − | $$[n]_q! = [1]_q [2]_q \ldots [n]_q | + | $$[n]_q! = \displaystyle\prod_{k=1}^n [k]_q=[1]_q [2]_q \ldots [n]_q,$$ |
| − | where $[k]_q$ denotes a [[q-number|$q$-number | + | where $[k]_q$ denotes a [[q-number|$q$-number]]. |
=Properties= | =Properties= | ||
| − | + | [[Q-derivative power rule]]<br /> | |
| − | + | [[Relationship between q-factorial and q-pochhammer]]<br /> | |
=See Also= | =See Also= | ||
[[q-number|$q$-number]]<br /> | [[q-number|$q$-number]]<br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=Q-number when a=n is a natural number|next=findme}}: (6.3) | ||
{{:q-calculus footer}} | {{:q-calculus footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 22:31, 16 June 2016
The $q$-Factorial is defined for a non-negative integer $k$ by $$[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
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.3)
