Differential Galois groups of confluent generalized hypergeometric equations: an approach using Stokes multipliers

Abstract

We explicitly compute the differential Galois groups of some families of generalized confluent hyper geometric equations by a method based on the asymptotic analysis of their irregular singularity at infinity. We obtain the Galois group directly from a particular set of topological generators. These are formal and analytic invariants of the equation, reflecting the asymptotic behaviour of the solutions. Our calculations yield classical groups as well as as the exceptional group G2.