I need to calculate the following integral: $$ \int_0^1 \int_0^1 \frac{1-\cos(2 \pi k_1 x) \cos(2 \pi k_2 y)}{4 \sin(\pi k_1)^2 + 4 \sin( \pi k_2)^2} dk_1 dk_2 $$ I have tried to use some contour integral techniques, but without much success. Any help will be appreciated.
2026-04-07 18:09:02.1775585342
Help computing an integral for Green's function of a discrete Laplacian on a square lattice
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