Abstract
In this paper we compute the values of series of the form \(S_k = \mathop \Sigma \limits_{n = 0}^\infty \tfrac{{(2n + 1)^k }}{{1 + e^{(2n + 1)\pi } }}\) if k ε ℕ is odd. This was done by Glaisher [4] if k ≡ 1 (mod 4), but if k ≡ 3 (mod 4) the result seems to be new.
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Literatur
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© 1985 Springer-Verlag
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Schoißengeier, J. (1985). Der Numerische Wert Gewisser Reihen. In: Hlawka, E. (eds) Zahlentheoretische Analysis. Lecture Notes in Mathematics, vol 1114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101652
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DOI: https://doi.org/10.1007/BFb0101652
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