The Ramanujan Journal

, Volume 26, Issue 2, pp 193–207

On the evaluation of Tornheim sums and allied double sums

Article

DOI: 10.1007/s11139-011-9302-5

Cite this article as:
Basu, A. Ramanujan J (2011) 26: 193. doi:10.1007/s11139-011-9302-5

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 functionEuler sumsRecursion formulasTornheim sums

Mathematics Subject Classification (2000)

40A2540B0511M9933E99

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

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