The Pochhammer symbol is notation used for both rising and falling factorials, e.g. in defining basic hypergeometric series and related special functions. This tag is also appropriate for questions about the $q$-Pochhammer symbol, which plays a similar role in defining $q$-hypergeometric series, etc.
The Pochhammer symbol is the notation used for the rising factorial:
$$(x)^n=x(x+1)\dots(x+n-1)$$
and the falling factorial:
$$(x)_n=x(x-1)\dots(x-n+1)$$
The $q$-Pochhammer symbol, also known as the $q$-shifted factorial, is defined by:
$$ (a;q)_n = \prod\limits_{k=0}^{n-1} (1-aq^k) $$
The Euler function $\phi(q)$ can be written as $(q;q)_\infty$.
