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arXiv · 2005.04227

Some Additions to a Family of Sums and Integrals related to Hurwitz' Zeta Function(s), Euler polynomials and Euler Numbers

Michael Milgram
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Abstract

Integrals involving the kernel function $sech (\pi x)$ over a semi-infinite range are of general interest in the study of Riemann's function $\zeta(s)$ and Hurwitz' function $\zeta(s,a)$. Such integrals that include the $arctan$ and $log$ functions in the integrand are evaluated here in terms of $\zeta(s,a)$, thereby adding some new members to a known family of related integrals. A claimed connection between $\zeta(s)$ of odd integer argument and such integrals is verified.

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Michael Milgram. 2020-05-09. Some Additions to a Family of Sums and Integrals related to Hurwitz' Zeta Function(s), Euler polynomials and Euler Numbers. https://arxiv.org/abs/2005.04227

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