Does the following double summation over x, x' (both integers) converge? $\sum\limits_{x=-\infty}^\infty \sum\limits_{x'=-\infty}^\infty \frac{Sin^2(2 \pi(x-x'))}{(x-x')^2}$. If so evaluate the sum. I understand that when $x \ne x'$ the sum is trivially 0. But I am unable to evaluate it generally. I believe I should get a Kronecker Delta, but am unable to prove it analytically.


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