Pochhammer

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The Pochhammer symbol $(a)_n$ is a notation that denotes the "rising factorial" function. It is defined by $$(a)_n = \dfrac{\Gamma(a+n)}{\Gamma(a)},$$ where $\Gamma$ denotes gamma.

Properties[edit]

Sum of reciprocal Pochhammer symbols of a fixed exponent
Pochhammer symbol with non-negative integer subscript

Notes[edit]

We are using this symbol to denote the rising factorial (following the notation used by Abramowitz&Stegun and Mathematica) as opposed to denoting the falling factorial (as Wikipedia does).

References[edit]