Computation of the Mordell-Tornheim zeta values

Petojević, Aleksandar; Srivastava, H.

doi:10.1090/S0002-9939-08-09350-7

Computation of the Mordell-Tornheim zeta values
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by Aleksandar Petojević and H. M. Srivastava PDF

Proc. Amer. Math. Soc. 136 (2008), 2719-2728 Request permission

Abstract:

In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values: \[ \zeta _{MT,r}(s_1,\; \cdots ,s_r;s) :=\sum _{m_1,\; \cdots , m_r=1}^\infty \frac {1}{m_1^{s_1}\; \cdots m_r^{s_r}(m_1+\cdots +m_r)^s}\] for the special cases \[ \zeta _{MT,r}(1,\; \cdots ,1;s) \qquad \text {and} \qquad \zeta _{MT,r}(0,\; \cdots ,0;s).\] Some interesting (known or new) consequences and illustrative examples are also considered.

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