Laguerre-Freud Equations for three families of hypergeometrical discrete orthogonal polynomials

TL;DR

This paper derives Laguerre-Freud equations for three families of hypergeometrical discrete orthogonal polynomials using Cholesky factorization of their moment matrices, expanding understanding of their structural properties.

Contribution

It introduces new Laguerre-Freud equations specific to hypergeometrical discrete orthogonal polynomials based on their moment matrices.

Findings

Derived Laguerre-Freud equations for three hypergeometrical polynomial families

Connected moments to generalized hypergeometrical functions

Enhanced structural understanding of these orthogonal polynomials

Abstract

The Cholesky factorization of the moment matrix is considered for discrete orthogonal polynomials of hypergeometrical type. We derive the Laguerre-Freud equations when the first moments of the weights are given by the ${}_1F_2$, ${}_2F_2$ and ${}_3F_2$ generalized hypergeometrical functions.