Generating functions of orthogonal polynomials in higher dimensions

TL;DR

This paper derives explicit generating functions for Clifford-Hermite and Clifford-Gegenbauer polynomials, two key classes of orthogonal polynomials in higher dimensions within Clifford analysis, enhancing understanding of their structure.

Contribution

The paper provides the first explicit generating functions for these two classes of higher-dimensional orthogonal polynomials in the Clifford analysis framework.

Findings

Explicit generating functions for Clifford-Hermite polynomials

Explicit generating functions for Clifford-Gegenbauer polynomials

Advances in higher-dimensional orthogonal polynomial theory

Abstract

In this paper two important classes of orthogonal polynomials in higher dimensions using the framework of Clifford analysis are considered, namely the Clifford-Hermite and the Clifford-Gegenbauer polynomials. For both classes an explicit generating function is obtained.