Difference and differential equations for deformed Laguerre–Hahn orthogonal polynomials on the unit circle

Sequences of orthogonal polynomials on the unit circle whose Caratheodory function satisfies a Riccati-type differential equation with polynomial coefficients are studied. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of reflection parameters, an...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 44; no. 46; pp. 465204 - 12
Main Authors Branquinho, A, Rebocho, M N
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 18.11.2011
IOP
Subjects
Deformation
Difference equations
Differential equations
Exact sciences and technology
Functions (mathematics)
Mathematical analysis
Physics
Polynomials
Reflection
Sequences
Circle
Deformation
Difference equations
Laguerre polynomials
Riccati equations
Differential equations
Polynomial equation
Orthogonal polynomial
Online AccessGet full text

Cover

More Information
Summary:Sequences of orthogonal polynomials on the unit circle whose Caratheodory function satisfies a Riccati-type differential equation with polynomial coefficients are studied. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of reflection parameters, and we analyze the continuous differential equations that arise when deformations through a dependence on a parameter t occur.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/44/46/465204