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Computation of the Mordell-Tornheim zeta values

Author(s): Aleksandar Petojevic; H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 136 (2008), 2719-2728.
MSC (2000): Primary 11M06, 33E20; Secondary 11B73, 33B15
Posted: April 10, 2008
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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, Podgoricka 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
Email: harimsri@math.uvic.ca

DOI: 10.1090/S0002-9939-08-09350-7
PII: S 0002-9939(08)09350-7
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
Posted: April 10, 2008
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2008, American Mathematical Society

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