English

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.

Keywords

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}
}
R2 v1 2026-06-28T16:01:54.867Z