Characterizations of classical orthogonal polynomials on quadratic lattices

TL;DR

This paper characterizes classical orthogonal polynomials on quadratic lattices using a matrix approach, recovering known characterizations and introducing a new one, while deriving recurrence relation coefficients.

Contribution

It provides a unified matrix-based framework for characterizations and introduces a novel characterization of these polynomials.

Findings

Recovered Hahn, Geronimus, Tricomi, and Bochner characterizations

Derived three-term recurrence relation coefficients

Presented a new characterization of classical orthogonal polynomials

Abstract

This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new characterization is also presented. From the Bochner type characterization we derive the three-term recurrence relation coefficients for these polynomials.