Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation
Classical Analysis and ODEs
2024-04-24 v2 Mathematical Physics
math.MP
Abstract
This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Pi\~neiro, 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.
Cite
@article{arxiv.2404.13958,
title = {Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation},
author = {Amílcar Branquinho and Juan EF Díaz and Ana Foulquié-Moreno and Manuel Mañas},
journal= {arXiv preprint arXiv:2404.13958},
year = {2024}
}