q-gamma function

Summary

The $q$-gamma function $\Gamma_q$ is a q-analog of the gamma function. It is a quotient of two q-Pochhammer symbols and satisfies $\Gamma_q(x + 1) = [x]_q\, \Gamma_q(x)$, where $[x]_q = \frac{1 - q^x}{1 - q}$ is the $q$-number. As $q \to 1^-$ it tends to $\Gamma(x)$. It appears throughout the theory of basic hypergeometric series.