Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials

Abstract

The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ρ0=2F1a,bc+1;η. For the Gauss hypergeometric discrete orthogonal polynomials, also known as generalized Hahn of type I, Laguerre–Freud equations are found, and the differences with the equations found by Dominici and by Filipuk and Van Assche are provided.

Keywords

• discrete orthogonal polynomials
• Pearson equations
• Cholesky factorization
• Laguerre–Freud equations
• hypergeometric functions
• tau functions