Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line

Branquinho, A.; Paiva, Anabela; Rebocho, M. N.

http://hdl.handle.net/10400.6/9004

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Authors

Branquinho, A.

Paiva, Anabela

Rebocho, M. N.

Abstract(s)

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.

Keywords

Orthogonal polynomials on the real line Stieltjes function Riccati differential equation Matrix Sylvester differential equations

URI

http://hdl.handle.net/10400.6/9004

Citation

A. Branquinho, A. Paiva, and M.N. Rebocho, Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line, Applied Mathematics and Computation 219 (17) (2013), 9118-9131.