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- Second- order differential equations in the Laguerre-Hahn classPublication . Rebocho, Maria das Neves; Branquinho, A.; Paiva, Anabela; Foulquie-Moreno, AnaLaguerre-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.
- Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real linePublication . Branquinho, A.; Paiva, Anabela; Rebocho, M. N.Matrix Sylvester differential equations are introduced in the study of Laguerre-Hahn orthogonal polynomials. Matrix Sylvester differential systems are shown to yield representations for the Laguerre-Hahn orthogonal polynomials. Lax pairs are given, formed from the differential system and the recurrence relation, that yield discrete non-linear equations for the three term recurrence relation coefficients of the Laguerre-Hahn orthogonal polynomials.