The Ramanujan Journal

, 17:163

An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers

Article

DOI: 10.1007/s11139-008-9130-4

Cite this article as:
Komori, Y. Ramanujan J (2008) 17: 163. doi:10.1007/s11139-008-9130-4

Abstract

A surface integral representation of the Mordell-Tornheim double zeta function is given, which is a direct analogue of a well-known integral representation of the Riemann zeta function of Hankel’s type. As an application, we investigate its values and residues at integers, where generalizations of a generating function of Bernoulli numbers naturally appear.

Keywords

Mordell-Tornheim double zeta functionAnalytic continuationIntegral representation

Mathematics Subject Classification (2000)

11M4130B40

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan