Shifted Appell sequences in Clifford analysis

TL;DR

This paper extends the theory of Appell sequences in Clifford analysis by proving that for any monogenic polynomial, there exists an associated Appell sequence starting with it, enriching the structure of monogenic polynomial sequences.

Contribution

It demonstrates the existence of Appell sequences of monogenic polynomials starting from any given monogenic polynomial in Clifford analysis.

Findings

Established the existence of Appell sequences for all monogenic polynomials.

Extended previous work on monogenic polynomial sequences.

Provided a constructive approach for generating Appell sequences.

Abstract

This paper is a continuation of [D. Pe\~{n}a Pe\~{n}a, On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function, arXiv:1102.1833], in which we prove that for every monogenic polynomial $\mathbf{P}_k(x)$ of degree $k$ in $\mathbb R^{m+1}$ there exists a sequence of monogenic polynomials $\{M_n(x)\}_{n\ge0}$ satisfying the Appell condition such that $M_0(x)=\mathbf{P}_k(x)$.