On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle

In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection f...

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 2; p. 246
Main Authors Garza, Lino G., Garza, Luis E., Huertas, Edmundo J.
Format Journal Article
LanguageEnglish
Published MDPI AG 01.02.2020
Subjects
coherent pairs of measures
holonomic differential equations
orthogonal polynomials on the unit circle
spectral transformations
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Summary:In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8020246