Let p be a prime ≡ 1 (mod 4). The value of the infinite series is given in finite terms.

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Persistent URL dx.doi.org/10.1090/S0002-9939-1990-1019275-7
Journal Proceedings of the American Mathematical Society
Citation
Hardy, K. (Kenneth), & Williams, K.S. (1990). Evaluation of the infinite series. Proceedings of the American Mathematical Society, 109(3), 597–603. doi:10.1090/S0002-9939-1990-1019275-7