On Appell Sets and the Fueter-Sce Mapping

TL;DR

This paper establishes that Appell polynomials in Clifford algebras are the Fueter-Sce extensions of complex monomials and identifies conditions under which these extensions coincide for certain functions.

Contribution

It proves the equivalence between Appell polynomials and Fueter-Sce extensions for specific functions in Clifford algebras, clarifying their relationship.

Findings

Appell polynomials are Fueter-Sce extensions of z^k

Conditions identified for when extensions coincide

Provides a link between Clifford algebra polynomials and complex functions

Abstract

It is proved, that the recently discussed Appell polynomials in Clifford algebras are the Fueter-Sce extension of the complex monomials z^k. Furthermore, it is shown, for which complex functions the Fueter-Sce extension and the extension method using Appell polynomials coincide.