# Gevrey and formal Nilsson solutions of $A$-hypergeometric systems

## TL;DR

This paper explores the relationship between Gevrey and formal Nilsson solutions of $A$-hypergeometric systems, establishing conditions under which these solution spaces coincide and providing new insights into their structure.

## Contribution

It demonstrates that Gevrey solutions are contained within formal Nilsson solutions and identifies conditions for their equality, advancing understanding of $A$-hypergeometric systems.

## Key findings

- Gevrey solutions are contained in formal Nilsson solutions
- Under certain conditions, these solution spaces are equal
- New results on formal Nilsson solutions are established

## Abstract

We prove that the space of Gevrey solutions of an $A$--hypergeometric system along a coordinate subspace is contained in a space of formal Nilsson solutions. Moreover, under some additional conditions, both spaces are equal. In the process we prove some other results about formal Nilsson solutions.