%0 Journal Article
%T Jackson's $(-1)$-Bessel functions with the Askey-Wilson algebra setting
%A Fethi Bouzeffour
%J Mathematics
%D 2013
%I arXiv
%X The aim of this work is to study new functions arising from the limit transition of the Jackson's $q$-Bessel functions when $q\rightarrow -1$. These functions coincide with the $cas$ function for particular values of their parameters. We prove also that these functions are eigenfunction of differential-difference operators of Dunkl-type. Further, we consider special cases of the Askey-Wilson algebra $AW(3)$ that have these operators (up to constants) as one of their three generators and whose defining relations are given in terms of anticommutators.
%U http://arxiv.org/abs/1310.8523v3