Does anyone have a closed form formula for the double series $$\sum_{n=0}^\infty\sum_{m=0}^\infty \frac{(-1)^{m+n}}{(2m+1)^3(2n+1)^3}\cos\left(\pi t \sqrt{(2m+1)^2+(2n+1)^2}\right)?$$ This is related to a solution of a two dimensional wave equation.
2026-04-09 04:07:20.1775707640
Closed form formula for a double series related to wave equation
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