On Stokes Matrices in terms of Connection Coefficients

TL;DR

This paper presents a method to compute Stokes multipliers for rank-one linear ODE systems directly from connection coefficients of related hypergeometric systems, removing previous genericness restrictions.

Contribution

It extends existing methods to calculate Stokes matrices without assuming generic conditions on the residue matrix at zero.

Findings

Explicit formula for Stokes multipliers in terms of connection coefficients

Method applicable to non-generic residue matrices

Advances the understanding of hypergeometric and linear ODE systems

Abstract

The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness assumptions on the residue matrix at zero, by an extension of the method of [3].