Gevrey expansions of hypergeometric integrals I

F. J. Castro-Jimenez, M. Granger

Published 2012-12-06, updated 2013-02-05Version 2

We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains are one dimensional. We prove that any Gevrey series solution along the singular support of the system is the asymptotic expansion of a holomorphic solution given by a carefully chosen integral representation.