I am trying to evaluate the integral ${1 \over2 \pi i} \int f(\nu)\,d\nu $; where $f(\nu) = {\pi \cot(\pi \nu) \over z^2-\nu^2}$
This integral is on the rectangle contour from $(-N- {1\over2})\leq x \leq (N+ {1\over2})$, and $-N\leq y \leq N $
2026-03-29 07:38:55.1774769935
How to calculate the residue of this function with this rectangle contour?
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