, Volume 26, Issue 2, pp 193-207
Date: 26 May 2011

On the evaluation of Tornheim sums and allied double sums

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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.