Fourier transforms of orthogonal polynomials on the cone

Abstract

The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal polynomials on the cone such as Laguerre polynomials on the cone and Jacobi polynomials on the cone and to define two new families of multivariate orthogonal functions by using Parseval's identity. Also, the obtained results are expressed in terms of the continuous Hahn polynomials.

22 pages. arXiv admin note: text overlap with arXiv:2206.13893