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# A Double Sum

Prove that:

$\sum _{m=1}^{\infty}\sum _{n=0}^{m-1}\dfrac{\left(-1\right)^{m-n}}{\left(m^2-n^2\right)^2}=-\dfrac{17\pi^4}{1440}$

This is a part of the set Formidable Series and Integrals

Note by Julian Poon
1 year ago