Fueter's theorem: the saga continues

TL;DR

This paper extends Fueter's theorem to higher order cases, incorporating an additional monogenic factor, thereby broadening the theorem's applicability in quaternionic and Clifford analysis.

Contribution

The paper introduces an extension of Fueter's theorem to higher order cases with an extra monogenic factor, advancing the theoretical framework of Clifford analysis.

Findings

Extended Fueter's theorem to higher order cases

Proved Fueter's theorem with an additional monogenic factor

Enhanced understanding of monogenic functions in Clifford analysis

Abstract

In this paper is extended the original theorem by Fueter-Sce (assigning an $\mathbb R_{0,m}$-valued monogenic function to a $\mathbb C$-valued holomorphic function) to the higher order case. We use this result to prove Fueter's theorem with an extra monogenic factor $P_k(x_0,\underline x)$.