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Computation of the Mordell-Tornheim zeta values

Authors:	Aleksandar Petojevic H. M. Srivastava

Affiliation:	Faculty of Education, University of Novi Sad, Podgoricka 4, YU-25000 Sombor, Serbia ; Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

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

Keywords:	Mordell-Tornheim zeta values Riemann zeta function gamma function Stirling numbers of the first kind polygamma functions integral representations recursion formulas monotone convergence theorem.

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