AN INTEGRAL REPRESENTATION OF MULTIPLE HURWITZ-LERCH ZETA FUNCTIONS AND GENERALIZED MULTIPLE BERNOULLI NUMBERS

Abstract

A surface integral representation of a multiple generalization of the Hurwitz–Lerch zeta function is given, which is a direct analogue of the well-known contour integral representation of the Riemann zeta function of Hankel's type. From this integral representation, we derive a detailed description of the set of its possible singularities. In addition, we present two formulae for special values of the zeta function at non-positive integers in terms of generalizations of Bernoulli numbers. These results are refinements of previously known ones.