The Pochhammer symbol is the notation used for rising and falling factorials. The $q$-Pochhammer symbol is the $q$-analog.

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 $(q;q)_\infty$.

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