Jacobi-Pi\~neiro Multiple Orthogonal Polynomials on the simplex
Classical Analysis and ODEs
2026-01-28 v1 Numerical Analysis
Numerical Analysis
Abstract
It is known that Rodrigues formulas provide a very powerful tool to compute orthogonal polynomials with respect to classical weights. We provide an example of bivariate multiple polynomials on the simplex defined via a Rodrigues formula. This approach offers a natural generalization of Jacobi--Pi\~neiro polynomials to the multivariate setting. Moreover, we apply these polynomials to the study of the bivariate Hermite--Pad\'e problem on the triangle.
Keywords
Cite
@article{arxiv.2601.19416,
title = {Jacobi-Pi\~neiro Multiple Orthogonal Polynomials on the simplex},
author = {Lidia Fernández and Ana Foulquié-Moreno and Juan Antonio Villegas},
journal= {arXiv preprint arXiv:2601.19416},
year = {2026}
}