Two-variable -1 Jacobi polynomials

被引：1

作者：

Genest, Vincent X. ^{[1
]}

Lemay, Jean-Michel ^{[1
]}

Vinet, Luc ^{[1
]}

Zhedanov, Alexei ^{[2
]}

机构：

[1] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada

[2] Donetsk Inst Phys & Technol, UA-340114 Donetsk, Ukraine

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2015年 / 26卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

33C50; bivariate orthogonal polynomials; Big -1 Jacobi polynomials; KRALL-SHEFFER POLYNOMIALS; LIMIT;

D O I：

10.1080/10652469.2015.1013034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A two-variable generalization of the Big -1 Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big -1 Jacobi polynomials. Their orthogonality measure is obtained. Their bispectral properties (eigenvalue equations and recurrence relations) are determined through a limiting process from the two-variable Big q-Jacobi polynomials of Lewanowicz and Wozny. An alternative derivation of the weight function using Pearson-type equations is presented.

引用

页码：411 / 425

页数：15

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