Two-variable $-1$ Jacobi polynomials
Classical Analysis and ODEs
2015-06-18 v1 Mathematical Physics
math.MP
Abstract
A two-variable generalization of the Big Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big 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 -Jacobi polynomials of Lewanowicz and Wo\'zny. An alternative derivation of the weight function using Pearson-type equations is presented.
Cite
@article{arxiv.1411.7299,
title = {Two-variable $-1$ Jacobi polynomials},
author = {Vincent X. Genest and Jean-Michel Lemay and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:1411.7299},
year = {2015}
}
Comments
13 pp