The Ramanujan Journal

, Volume 26, Issue 2, pp 193–207

On the evaluation of Tornheim sums and allied double sums


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


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.


Riemann Zeta functionEuler sumsRecursion formulasTornheim sums

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

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