buddies, I meet an inverse Mellin transform problem with Gauss hypergeometric function in term of $z$ as follows:
$ \mathcal M^{-1}\left\{ {\beta ^{ - z}}{\Gamma ^a}\left( z \right){\left[ {{}_2{F_1}\left( {m,z;1;\alpha} \right)} \right]^a}\right\}$,
where ${}_2{F_1}\left( { \cdot, \cdot; \cdot; \cdot } \right)$ is the Gauss hypergeometric function.
I am very appreciated of any helps!