Jackson's (-1)-Bessel functions with the Askey-Wilson algebra setting

Journal Article
Chorfi,, Bouzeffour, F Jedidi, W . 2015
المجلة \ الصحيفة: 
ADVANCES IN DIFFERENCE EQUATIONS
رقم العدد: 
Article Number: 268
مستخلص المنشور: 

Abstract

This work is devoted to the study of some functions arising from a limit transition of the Jackson q-Bessel functions when q tends to -1. These functions coincide with the so-called cas function for particular values of parameters. We prove that there are eigenfunctions of differential-difference operators of Dunkl-type. Also we consider special cases of the Askey-Wilson algebra , which have these operators (up to constants) as one of their three generators and whose defining relations are given in terms of anti-commutators.