Pochhammer symbol

Summary

The Pochhammer symbol $(a)_n$ is the rising factorial $a (a + 1) \cdots (a + n - 1)$, a product of $n$ consecutive terms that go up by $1$ starting at $a$. It is the basic building block of the hypergeometric series, whose coefficients are quotients of Pochhammer symbols. For $a$ not a non-positive integer it equals $\Gamma(a + n)/\Gamma(a)$, which ties it to the gamma function. In combinatorics the same notation $(x)_n$ often stands for the falling factorial instead, so one has to check the convention of each text.