On the evaluation of Tornheim sums and allied double sums |
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Authors: | Ankur Basu |
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Institution: | (1) College of Economics and Management, YanShan University, Qinhuangdao, 066004, People’s Republic of China;(2) College of Science, YanShan University, Qinhuangdao, 066004, People’s Republic of China; |
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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. |
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