Q-Pochhammer

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The $q$-Pochhammer symbol $[a]_{n,q}$ is defined for $n=0$ by $[a]_{0,q}=1$, for $n=1,2,3,\ldots$ by the formula $$[a]_{n,q}= \displaystyle\prod_{k=0}^{n-1} [a+k]_q = \left(\dfrac{1-q^a}{1-q} \right) \left( \dfrac{1-q^{a+1}}{1-q} \right) \ldots \left( \dfrac{1-q^{a+n-1}}{1-q} \right) ,$$ where $[a]_q$ denotes a $q$-number.

Notes[edit]

Mathworld and Mathematica define the "$q$-Pochhammer symbol" to be what we call the $q$-factorial.


$q$-calculus