Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation

2024/04/22 by Amílcar Branquinho, Branquinho, Amílcar, Juan E. F. Díaz +5 · 1 citation
Mathematics · #33C45 #33C47 #42C05 #47B36 #47B39 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2404.13958

openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.

Cited by

• Uvarov Perturbations for Multiple Orthogonal Polynomials of the Mixed Type on the Step-Line

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