On Stokes Matrices in terms of Connection Coefficients

Abstract

We study the classical problem of the computation of a complete system of Stokes matrices in terms of connection coefficients. Stokes matrices refer to a linear system of ODEs with Poincaré rank one and semi-simple leading matrix, while the connection coefficients connect solutions of the associated hypergeometric system of ODEs. The problem here is solved with no assumptions on the residue matrix at zero of the system of Poincaré rank one, so extending method and results of [4].