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

Consider the integral of the function (1) around a large circle of radius R>>b which avoids the singularities of ([itex]e^{z}[/itex]+1)[itex]^{-1}[/itex]. Use this result to determine the sum (2) and (3).

2. Relevant equations

(1) - f(z) = [itex]\frac{1}{(z^2-b^2)(e^z+1)}[/itex]

(2) - [itex]\sum[/itex][itex]\frac{1}{(2n+1)^2+a^2}[/itex] from 1 to ∞

(3) - [itex]\sum[/itex][itex]\frac{1}{(2n+1)^2}[/itex] from 1 to ∞

3. The attempt at a solution

I understand the basics of contour integration and using residues to evaluate them; however, with this particular question I am lost at where I should start. I think that the contour should be a circle obvioulsy but going from the contour to the summation has me confused.

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# Complex Integral Issue

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