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

DOI10.1007/S41980-022-00706-YarXiv2101.04059MaRDI QIDQ6358043

Iván Area, Rabïa Aktaş, Esra Güldoğan Lekesiz

Publication date: 26 December 2020

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.

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Other hypergeometric functions and integrals in several variables (33C70) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

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