Difference between revisions of "Q-factorial"
From specialfunctionswiki
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$$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ | $$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ | ||
where $(q;q)_k$ is the [[q-Pochhammer symbol]]. | where $(q;q)_k$ is the [[q-Pochhammer symbol]]. | ||
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Revision as of 06:58, 5 April 2015
The $q$-Factorial is defined for a non-negative integer $k$ by $$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ where $(q;q)_k$ is the q-Pochhammer symbol.
