A new class of three-variable orthogonal polynomials and their recurrences relations
type: Item
instance of: scholarly article
title: A new class of three-variable orthogonal polynomials and their recurrences relations
zbMATH Open document ID: 1168.42013
published in: Science in China. Series A
publication date: 2008-09-09T00:00:00Z
review text: The author studies a new class of three variable orthogonal polynomials, defined as eigenfunctions of a second order partial differential operator. These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron, and can be taken as an extension of the 2D Steiner domain. The polynomials can be viewed as Jacobi polynomials on such a domain. Three term relations are derived explicitly. The number of the individual terms, involved in the recurrences relations, are shown to be independent on the total degree of the polynomials. The numbers are now determined to be five and seven, with respect to two conjugate variables \(z,\bar{z}\) and a real variable \(r\), respectively. Three examples are discussed in detail, which can be regarded as the analogues of the Chebyshev polynomials of first and second kinds, and Legendre polynomials.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35P10
zbMATH DE Number: 5323379
zbMATH Keywords: 3D PDE eigen-problem
zbMATH Keywords: three variable Chebyshev polynomials
zbMATH Keywords: Legendre polynomial
zbMATH Keywords: Jacobi polynomial
zbMATH Keywords: recurrence relations
author: Jiachang Sun
reviewed by: Qutaibeh Katatbeh
MaRDI profile type: Publication
full work available at URL: s11425-007-0188-z
OpenAlex ID: W1489055878
cites work: Q4041914
cites work: Orthogonal polynomials of several variables
cites work: Orthogonal polynomials in two variables. Transl. from the 1988 Russian original by E. V. Pankratiev
cites work: Q4709673
cites work: Q5477466
cites work: Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
DOI: 10.1007/S11425-007-0188-Z
description: scientific article; zbMATH DE number 5323379