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Deformed Laguerre-Hahn orthogonal polynomials on the real line
Publication . Branquinho, A.; Rebocho, M. N.
We study families of orthogonal polynomials on the real line whose
Stieltjes functions satisfy a Riccati type differential equation with polynomial coefficients.
We derive discrete dynamical systems, obtained as a result of deformations
of the recurrence relation coefficients of the orthogonal polynomials related to the
above referred Stieltjes functions.
On the semiclassical character of orthogonal polynomials satisfying structure relations
Publication . Branquinho, A.; Rebocho, M. N.
We prove the semiclassical character of some sequences of orthogonal polynomials [...]
Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line
Publication . 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.
Structure relations for orthogonal polynomials on the unit circle
Publication . Branquinho, A.; Rebocho, M. N.
Structure relations for orthogonal polynomials on the unit circle are
studied. We begin by proving that semi-classical orthogonal polynomials on the
unit circle satisfy structure relations of the following type: [...]
Second- order differential equations in the Laguerre-Hahn class
Publication . Rebocho, Maria das Neves; Branquinho, A.; Paiva, Anabela; Foulquie-Moreno, Ana
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.
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Funding agency
Fundação para a Ciência e a Tecnologia
Funding programme
SFRH
Funding Award Number
SFRH/BPD/45321/2008