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arXiv · 1212.1410

Gevrey expansions of hypergeometric integrals I

F. J. Castro-Jimenez·M. Granger
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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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F. J. Castro-Jimenez, M. Granger. 2013-02-05. Gevrey expansions of hypergeometric integrals I. https://arxiv.org/abs/1212.1410

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