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

Abstract

The aim of this work is to study new functions arising from the limit transition of the Jackson's $q$-Bessel functions when $q\to -1$. 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.

This paper has been withdrawn by the author due to typo errors

References in corpus (2)

• A "missing" family of classical orthogonal polynomials
• The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case