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

arxiv: 1207.2055 · v1 · pith:KTDE7XKNnew · submitted 2012-07-09 · 🧮 math.CA

Comment on the sums S(n)=sumlimits_{k=-infty}^infty frac{1}{(4k+1)^n}

Z. K. Silagadze This is my paper

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keywords commentcvijovicexplicitexpressioninftyintegralklinowskimath

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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 $\zeta(2n+1)$.

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Comment on the sums S(n)=sumlimits_{k=-infty}^infty frac{1}{(4k+1)^n}

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