Shifted Appell sequences in Clifford analysis

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 $M_0(x)=\mathbf{P}_k(x)$.