Special functions associated with complex reflection groups

Journal Article

Bouzeffour, Fethi . 2014

• رابط المنشور على الويب: The Ramanujan Journal
• المجلة \ الصحيفة: http://link.springer.com/article/10.1007%2Fs11139-013-9481-3
• رقم العدد: , Issue 1
• رقم الإصدار السنوي: Volume 34
• الصفحات: , 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.