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Certain functional relations for the double harmonic series related to the double Euler numbers

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  09 April 2009

Hirofumi Tsumura
Hirofumi Tsumura
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan, e-mail: tsumura@comp.metro-u.ac.jp
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Abstract

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In this paper, we give certain analytic functional relations for the double harmonic series related to the double Euler numbers. These can be regarded as continuous generalizations of the known discrete relations obtained by the author recently.

Keywords

double Euler numbersdouble harmonic seriesMordell-Tornheim double zeta functionsRiemann zeta functionuniformly convergent series.

MSC classification

Secondary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section) 11M41: Other Dirichlet series and zeta functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 319 - 333
Copyright
Copyright © Australian Mathematical Society 2005

References

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