2021/07/04 by Itsaso Fernández‐Irisarri, Fernández-Irisarri, Itsaso, Manuel Mañas +1
Mathematics · Physics and Astronomy · #33C45 #33C47 #42C05 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2107.02177
openalex publication_date 2021/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The Cholesky factorization of the moment matrix is considered for the generalized Charlier, generalized Meixner, and Gauss hypergeometric discrete orthogonal polynomials. For the generalized Charlier, we present an alternative derivation of the Laguerre-Freud relations found by Smet and Van Assche. Third-order and second-order nonlinear ordinary differential equations are found for the recursion coefficient γn, that happen to be forms of the Painlevé deg-P\text V in disguise. Laguerre-Freud relations are also found for the generalized Meixner case, which are compared with those of Smet and Van Assche. Finally, the Gauss hypergeometric discrete orthogonal polynomials, also known as generalized Hahn of type I, are also studied. Laguerre-Freud equations are found, and the differences with the equations found by Dominici and by Filipuk and Van Assche are provided.