Difference between revisions of "Q-factorial"
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(Created page with "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-Pochha...") |
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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 | ||
$$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ | $$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ | ||
| − | where $(q;q)_k$ is the [[q-Pochhammer]] | + | where $(q;q)_k$ is the [[q-Pochhammer symbol]]. |
Revision as of 18:17, 27 July 2014
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.
