On Laguerre-Hahn affine orthogonal polynomials on the unit circle from matrix Sylvester equations

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 . The technique is based on the knowledge of the first-order differential equation for the Carathéodory functio...

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Bibliographic Details
Published inIntegral transforms and special functions Vol. 27; no. 2; pp. 78 - 93
Main Author Rebocho, M.N.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.02.2016
Taylor & Francis Ltd
Subjects
Compatibility
Differential equations
discrete Painlevé equations
Formalism
Functions (mathematics)
Hermitian linear functionals
Laguerre-Hahn affine class
Mathematical analysis
OPUC
Polynomials
Reflection coefficient
Sylvester equations
Transforms
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Summary: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 . The technique is based on the knowledge of the first-order differential equation for the Carathéodory function, combined with a re-interpretation, in the formalism of matrix Sylvester equations, of compatibility conditions for the differential systems satisfied by the polynomials.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2015.1092969