# Gevrey expansions of hypergeometric integrals II

## TL;DR

This paper investigates the Gevrey series solutions of irregular hypergeometric systems, showing they can be represented as asymptotic expansions of holomorphic solutions via specific integral representations.

## Contribution

It proves that Gevrey series solutions along coordinate hyperplanes are asymptotic expansions of holomorphic solutions expressed through integral representations.

## Key findings

- Gevrey series solutions are asymptotic to holomorphic solutions
- Integral representations can be constructed for these solutions
- Results apply under specific assumptions on the hypergeometric systems

## Abstract

We study integral representations of the Gevrey series solutions of irregular hypergeometric systems under certain assumptions. We prove that, for such systems, any Gevrey series solution, along a coordinate hyperplane of its singular support, is the asymptotic expansion of a holomorphic solution given by a carefully chosen integral representation.