A generalization of Fueter's theorem in Dunkl–Clifford analysis

Abstract

In this article, we first suggest an alternative approach to extend the original Fueter's theorem in Dunkl–Clifford analysis to a version of the higher order case. We then use this result to prove a generalized version of Fueter's theorem with an extra homogeneous Dunkl-monogenic polynomial P n (x 0, x ) in instead of the classical factor P n ( x ) in ℝ d .