, Volume 17, Issue 2, pp 163-183
Date: 12 Jul 2008

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

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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.