Rising factorial

In this article, the symbol ${\displaystyle (x)_{n}}$ is used to represent the falling factorial, and the symbol ${\displaystyle x^{(n)}}$ is used for the rising factorial. These conventions are used in combinatorics, although Knuth's underline and overline notations ${\displaystyle x^{\underline {n}}}$ and ${\displaystyle x^{\overline {n}}}$ are increasingly popular. In the theory of special functions (in particular the hypergeometric function) and in the standard reference work Abramowitz and Stegun, the Pochhammer symbol ${\displaystyle (x)_{n}}$ is used to represent the rising factorial.