  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.
