Jacobi-Pi\~neiro Multiple Orthogonal Polynomials on the simplex

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.