Complex versus real orthogonal polynomials of two variables

TL;DR

This paper investigates the relationship between complex and real orthogonal polynomials of two variables, analyzing their structural relations with examples like complex Hermite and disk polynomials.

Contribution

It provides a detailed study of the connection and structural relations between complex and real orthogonal polynomials in two variables, with illustrative examples.

Findings

Established the connection between complex and real orthogonal polynomials

Analyzed structural relations of complex orthogonal polynomials

Illustrated concepts using complex Hermite and disk polynomials

Abstract

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.