ON CONFLUENCES OF GENERAL HYPERGEOMETRIC SYSTEMS

Abstract

We extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hypergeometric systems. We see that the process of confluence comes from the geometry of the set of regular elements of the Lie algebra of complex general linear group. As a consequence, we give a geometric and group-theoretic view on the process of confluence for classical special functions.