To be a little more specific as to what I am looking at...it's basically:

∫ ∑s/[p(s-p)] where the sum is infinite (over p) and the limits of integration are from a-i∞ to a+i∞

I have about 4 or 5 integral/sums like this.

So instead of proving termwise integration is valid for each one...is there a more general approach?