Second-order differential equations in the Laguerre–Hahn class

• Published in: Applied numerical mathematics Vol. 94; pp. 16 - 32
• Main Authors: Branquinho, A., Foulquié Moreno, A., Paiva, A., Rebocho, M.N.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2015
• Subjects: Classical orthogonal polynomials; Orthogonal polynomials on the real line; Riccati differential equation; Semi-classical functionals; Riccati differential equation; Classical orthogonal polynomials; Semi-classical functionals; Orthogonal polynomials on the real line
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2015.03.002

Laguerre–Hahn families on the real line are characterized in terms of second-order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and their associated polynomials, as well as in terms of second-order differential equation for the functions of the second kind. Some characterizations of the classical families are derived.