Special functions associated with complex reflection groups

Journal Article
Bouzeffour, Fethi . 2014
المجلة \ الصحيفة: 
رقم العدد: 
, Issue 1
رقم الإصدار السنوي: 
Volume 34
, pp 39-55
مستخلص المنشور: 

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.

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