Pochhammer

From specialfunctionswiki
Revision as of 18:56, 18 December 2016 by Tom (talk | contribs)
Jump to: navigation, search

The Pochhammer symbol $(a)_n$ is a notation that denotes the "rising factorial" function. It is defined by $$\left\{ \begin{array}{ll} (a)_0 &= 1 \\ (a)_n \equiv a^{\overline{n}} &= \displaystyle\prod_{k=0}^{n-1} a+k=a(a+1)(a+2)\ldots(a+n-1). \end{array} \right.$$

Properties

Sum of reciprocal Pochhammer symbols of a fixed exponent

Notes

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

Abramowitz and Stegun