Characterizations of classical orthogonal polynomials on quadratic lattices

Abstract

This paper is devoted to characterizations of 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.