# Gevrey expansions of hypergeometric integrals I

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00762389
Contributor : Michel Granger <>
Submitted on : Tuesday, February 5, 2013 - 11:28:19 PM
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• HAL Id : hal-00762389, version 2

### Citation

Francisco-Jesus Castro-Jiménez, Michel Granger. Gevrey expansions of hypergeometric integrals I. 2012. ⟨hal-00762389v2⟩

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