A matrix Rodrigues formula for classical orthogonal polynomials in two variables

2006/10/03 by A. Alvarez de Morales, de Morales, A. Alvarez, Lidia Fernández +5
Computer Science · Mathematics · #42C05 (Primary) 33C50 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.math/0610128

openalex publication_date 2006/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Classical orthogonal polynomials in one variable can be characterized as the only orthogonal polynomials satisfying a Rodrigues formula. In this paper, using the second kind Kronecker power of a matrix, a Rodrigues formula is introduced for classical orthogonal polynomials in two variables.

Related

• Characterization of classical orthogonal polynomials in two variables
• Matrix valued polynomials generated by the scalar-type Rodrigues' formulas
• A class of matrix-valued polynomials generalizing Jacobi Polynomials
• Krall--type Orthogonal Polynomials in several variables
• Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation