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.

arXiv commentNew statements and proofs for Theorem 4.8 and Proposition 4.12. Corrected typos

References in corpus (8)

• Introduction to Stokes structures
• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Equivariant D-modules
• Periods for flat algebraic connections
• The rank of a hypergeometric system
• Isomorphism classes of A-hypergeometric systems
• Confluent A-hypergeometric functions and rapid decay homology cycles
• Gevrey expansions of hypergeometric integrals I

Cited by in corpus (1)

• Gevrey expansions of hypergeometric integrals I