Special functions associated with complex reflection groups

In this paper, we first review the theory of Dunkl operators for complex reflection groups and then the theory of hyper-Bessel functions, which are a particular case of Meijer's G-function and satisfy a higher order differential equation. Then we show that there exists a close relation between both theories. In fact, the components of the eigenfunctions of a Dunkl operator for a complex reflection group in the rank one case can be expressed in terms of hyper-Bessel functions.