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Authors
Advisor(s)
Abstract(s)
In this paper are derived recurrences for the reflection coefficients
of Laguerre–Hahn affine orthogonal polynomials on the unit circle,
including a form of the discrete Painlevé equations dPV . The
technique is based on the knowledge of the first-order differential
equation for the Carathéodory function, combined with a reinterpretation,
in the formalism of matrix Sylvester equations, of
compatibility conditions for the differential systems satisfied by the
polynomials.
Description
Keywords
Hermitian linear functionals OPUC Laguerre–Hahn affine class Sylvester equations discrete Painlevé equations
Pedagogical Context
Citation
M.N. Rebocho, On Laguerre-Hahn affine orthogonal polynomials on the unit circle from matrix Sylvester equations, Integral Transforms and Special Functions 27, no.2 (2016) 78-93.