English

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 1-1 Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big 1-1 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 qq-Jacobi polynomials of Lewanowicz and Wo\'zny. An alternative derivation of the weight function using Pearson-type equations is presented.

Keywords

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

R2 v1 2026-06-22T07:13:24.677Z