Fourier transforms of some special functions in terms of orthogonal polynomials on the simplex and continuous Hahn polynomials

TL;DR

This paper develops Fourier transforms for multivariate orthogonal polynomials on the simplex, introducing a new family of orthogonal functions through Parseval's identity and recurrence relations.

Contribution

It presents a novel Fourier transform framework for multivariate orthogonal polynomials and constructs a new family of orthogonal functions.

Findings

Derived Fourier transforms for multivariate orthogonal polynomials on the simplex

Established recurrence relations for the new orthogonal functions

Connected the transforms to continuous Hahn polynomials

Abstract

In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.