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.
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