Pochhammer Symbol - Generalizations

Generalizations

The Pochhammer symbol has a generalized version called the generalized Pochhammer symbol, used in multivariate analysis. There is also a q-analogue, the q-Pochhammer symbol.

A generalization of the falling factorial in which a function is evaluated on a descending arithmetic sequence of integers and the values are multiplied is:

where −h is the decrement and k is the number of factors. The corresponding generalization of the rising factorial is

This notation unifies the rising and falling factorials, which are k/1 and k/−1, respectively.