# Complex residue integral

1. Jun 7, 2009

### zetafunction

1. The problem statement, all variables and given/known data

i need to calculate the inverse Mellin transform $$\oint ds {x^{-s}}\frac{1}{\Gamma(s)cos(\pi s/2)}$$

2. Relevant equations

I can use Cauchy's integral theorem,

3. The attempt at a solution

i know that Gamma function has poles at -1,-2,-3, .... and that the cosine term has poles at every integer the question is how could i expand Gamma function and cosine term in order to obtain the complex integral.

2. Jun 7, 2009

### HallsofIvy

Staff Emeritus
What path is the integral taken over and, in particular, what integers are contained inside that path?