Q-factorial

The $q$-Factorial is defined for a non-negative integer $k$ by $$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ where $(q;q)_k$ is the q-Pochhammer symbol.

$q$-calculus

$q$-Binomial

$q$-Gamma

$q$-factorial

$q$-Pochhammer