# Numerical contour integral

I am trying to compute the double integral for fixed $$m,z>0$$:

``   Integrate[(Gamma[y/2] Sqrt[Gamma[3 - y]/Gamma[y]])/   Gamma[(3 - y)/2] z^(3 - y)    (Exp[-m x] - 1) x^(y - 3)/x, {x, 0, \[Infinity]},{y,    3/2 - I \[Infinity], 3/2 + I \[Infinity]}] ``

The integral over $$x$$ can be done analytically, and the result depends on the product $$mz$$, so there is effectively just one parameter. The $$x$$ integral needs to be split into two regions I suspect, and in one region the contour of the $$y$$ integral would need to be deformed so that it remains convergent. Since the $$y$$ integral involves complicated branch cuts, I wanted to be able to do it numerically for a range of $$mz$$, to get a least a few digits of precision. I am having difficulty getting stable results numerically tho.