Some Appell–Dunkl Sequences

Abstract

AbstractSome examples of Appell–Dunkl sequences are shown using determined operators. Specifically, Appell–Dunkl sequences whose generating functions are of the form $$E_{\alpha }(xt)/(1\pm t^m)$$ E α ( x t ) / ( 1 ± t m ) , where the function $$E_{\alpha }(xt)$$ E α ( x t ) is given in terms of Bessel functions. Particular cases of these examples are also generated by means of the inverse of the Dunkl operator.