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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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Infinite sum related to Hurwitz Zeta

I want to evaluate the following sum: \begin{equation} \sum_{-\infty}^{\infty}\frac{(-1)^n}{(n+a)^2} \end{equation} Where $a\in\mathbb{R}$ is not an integer. Such is similar to $\zeta(2,a)$, but it ra …