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arXiv · 1310.8523

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

Fethi Bouzeffour
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Abstract

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

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BibTeXRIS

Fethi Bouzeffour. 2016-09-29. Jackson's $(-1)$-Bessel functions with the Askey-Wilson algebra setting. https://arxiv.org/abs/1310.8523

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