Bessel functions of two variables: some power series and plots

Abstract

For a finite reflection group G there is a rich theory developed by Dunkl, Heckman and Opdam leading to the notion of a commuting set of Bessel differential operators. These systems play an important role in the study of Calogero-Moser systems and other problems of physical interest. When G acts on the line one recovers the usual Bessel function with a well known power series expansion at the origin. We obtain some such expansions in the case of G = A2 acting in the plane and we use these to produce plots of some of these functions.