I am trying to evaluate the reverse Mellin's transform for the pochhammer symbol.
I got to this equation: $\frac{1}{2\pi \cdot i} \int_{\sigma-i\infty}^{\sigma+i\infty}\frac{\Gamma(s)} {\Gamma(s+k+1)} y^{-s}ds$. $\sigma>0$ and $k$ can be any positive integer.
I don't know how to proceed. Could anyone help me with this evaluation?
I am not sure if I am heading the right direction
I tried $\Gamma(s)=\int^\infty_0e^{-u}u^s\frac{du}{u}$ and $\Gamma(s+k+1)=\int^\infty_0e^{-u}u^{s+k+1}\frac{du}{u}$
I try to solve the $\frac{\int^\infty_0e^{-u}u^s\frac{du}{u}}{\int^\infty_0e^{-u}u^{s+k+1}\frac{du}{u}}$, but not sure what I can do next.