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arXiv · 1207.2055

Comment on the sums $S(n)=\sum\limits_{k=-\infty}^\infty \frac{1}{(4k+1)^n}$

Z. K. Silagadze
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Abstract

This is a comment on the papers N. D. Elkies, Amer. Math. Monthly 110 (2003), 561-573 and Cvijovic and J. Klinowski, J. Comput. Appl. Math. 142 (2002), 435-439. We provide an explicit expression for the kernel of the integral operator introduced in the first paper. This explicit expression considerably simplifies the calculation of S(n) and enables a simple derivation of Cvijovic and Klinowski's integral representation for $ζ(2n+1)$.

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Z. K. Silagadze. 2012-07-09. Comment on the sums $S(n)=\sum\limits_{k=-\infty}^\infty \frac{1}{(4k+1)^n}$. https://doi.org/10.1515/gmj-2012-0023

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