I would like to calculate the inverse Mellin transform of the following function ($a$ being a real positive number):
$$f(s)=(2 \pi)^{-s} \cos(\frac{\pi s}{2}) \Gamma(s) \frac{1-a^{s-1}}{1-a^{-s}}.$$
How can I calculate it?
Inverse is the following integral ($\mathcal{Re}(c)>0$):
$$[\mathcal{M}^{-1} f] (x) =\frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} (2 \pi)^{-s} \cos(\frac{\pi s}{2}) \Gamma(s) \frac{1-a^{s-1}}{1-a^{-s}} x^{-s} ds.$$
(I do not have Matlab to ask for a result...)