(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm having difficulties with the integral sinh(ax)/sinh(pi*x) from -inf to inf.

2. Relevant equations

3. The attempt at a solutionI've attached my attempt at a solution. First, I'm not sure that it's true that for the representation of the function f(z)=sinh(az)/sinh(pi*z) that it's true that the contributions from the vertical edges go to 0. Also, when I get to the end, I can't find a nice way to have an exponential factor times the original integral = the sum of residues... Any hints? Thanks.

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# Contour integral w/ sinh in numerator & denominator

Can you offer guidance or do you also need help?

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