Fueter's theorem: the saga continues

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 $P_k(x_0,\underline x)$.