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Converting a 2D lattice sum into a sum over 1D lattice sums in a circle
I'm working on a physics problem. I have a lattice sum, which in 1D is a sum over a linear chain. It reads
$$
f_k = \sum_{n=1}^\infty \frac{2\cos(kn)}{n^3}.
$$
This can be written in terms of ...
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