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In the process of finding a solution to a mechanical problem I arrived at a contour integral. Then I had to use the residue theorem to solve the integral. Finally I got an integral with the following format:

$\oint_C f(z)\,\mathrm dz$ $f(z)=\frac{e^{(Az^N+Bz^{-N})}}{z-a},\qquad A,B\in \mathbb R,N\in \mathbb Z$

where $a$ is a constant and can be in/or out of the closed contour $C$. My problem is that how I should obtain the residue in both cases (when $a$ is in and out of the contour). Can I use the Laurent expansion? How should I treat the singularity at $z=0$? Thanks for hints in advance.

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    **@joriki** Thanks for editing the question. I thought it would be better to post the new problem as a new question. I'll post questions according to your advice.2011-07-14

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