Work

Discrete orthogonal polynomials related to Hahn difference operator

Year: 2026

Type: preprint

Abstract: This work studies general sequences of discrete orthogonal polynomials on linear lattices, including the so-called discrete Laguerre--Hahn orthogonal polynomials. We deduce the structure relations involving the orthogonal polynomials and their associated, as well as the explicit form of the fourth--order linear difference equation satisfied by these Laguerre--Hahn orthogonal polynomials. Furthermore, the particular cases corresponding to semiclassical and classical families of orthogonal polynomials, which lead to second--order difference equations, are also analyzed. Several examples illustrating the computation of the explicit coefficients of these difference equations for various families of orthogonal polynomials are also presented.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30933

Authors: Mañas-Mañas, J. F., Moreno-Balcázar, J. J., Rebocho, M. N., Rodr\'ıguez-Perales, C.

Institutions: University of Almería, University of Beira Interior, Centro de Matemática e Aplicações

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green