The Hadamard product of hypergeometric series

Typically a hypergeometric function is a multi-valued analytic function with algebraic singularities. In this paper we give a complete description of the Newton polytope of the polynomial whose zero set naturally contains the singular locus of a nonconfluent double hypergeometric series. We show in particular that the Hadamard multiplication of such series corresponds to the Minkowski sum of the Newton polytopes of polynomials which define their singularities. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.