On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function

Abstract

In this paper we aim at constructing a sequence $\{{\mathsf{M}}_n^k(x){\}}_{n\ge 0}$ of ${\mathbb{R}}_{0,m}$-valued polynomials which are monogenic in ${\mathbb{R}}^{m+1}$ satisfying the Appell condition (i.e. the hypercomplex derivative of each polynomial in the sequence equals, up to a multiplicative constant, its preceding term) but whose first term ${\mathsf{M}}_0^k(x)={\mathbf{P}}_k(\underline{x})$ is a ${\mathbb{R}}_{0,m}$-valued homogeneous monogenic polynomial in ${\mathbb{R}}^m$ of degree $k$ and not a constant like in the classical case. The connection of this sequence with the so-called Fueter's theorem will also be discussed.

10 pages, submitted for publication

References in corpus (2)

• On Appell Sets and the Fueter-Sce Mapping
• Fueter's theorem: the saga continues