Consider the analytic continuation of the factorial function $n!$ given by $\Gamma(z)$ (note $n!=\Gamma(n+1)$), and suppose $z=a^{-n}$, where $a,n\in\mathbb{N}$ are positive integers.
Are there any known properties/identities/functional identities of the Gamma function in this case? I have searched the web but cannot find anything at all.