The Ramanujan Journal

, Volume 26, Issue 2, pp 193–207

On the evaluation of Tornheim sums and allied double sums

Article

Abstract

The object of study in this paper is some Tornheim type sums \(\sum_{n=1}^{\infty}\sum_{m=1}^{\infty} \frac{1}{n^{r}m^{s}(n+m)^{t}}\) which are close relatives of the so-called Euler sums \(\sum_{n=1}^{\infty}\frac{1}{n^{s}}\sum_{m=1}^{\infty}\frac{1}{m^{t}}\). Closed form evaluations of several such double sums are obtained using elementary summation techniques earlier developed by the same author.

Keywords

Riemann Zeta function Euler sums Recursion formulas Tornheim sums 

Mathematics Subject Classification (2000)

40A25 40B05 11M99 33E99 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.1/45-c/o Ranjit BasuChandannagar, Dist. HooghlyIndia

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