Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Computation of the Mordell-Tornheim zeta values

Authors: Aleksandar Petojevic and H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 136 (2008), 2719-2728
MSC (2000): Primary 11M06, 33E20; Secondary 11B73, 33B15
Published electronically: April 10, 2008
MathSciNet review: 2399033
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Abstract: In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values:

$\displaystyle \zeta_{MT,r}(s_1,\; \cdots ,s_r;s) :=\sum_{m_1,\; \cdots, m_r=1}^\infty\frac{1}{m_1^{s_1}\; \cdots m_r^{s_r}(m_1+\cdots +m_r)^s}$

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.

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Additional Information

Aleksandar Petojevic
Affiliation: Faculty of Education, University of Novi Sad, Podgorička 4, YU-25000 Sombor, Serbia
Email: apetoje@ptt.yu

H. M. Srivastava
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

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.
Received by editor(s): June 20, 2007
Published electronically: April 10, 2008
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society