On differential equations associated with perturbations of orthogonal polynomials on the unit circle

Lino G. Garza, Luis E. Garza, Edmundo J. Huertas

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number246
JournalMathematics
Volume8
Issue number2
DOIs
Publication statusPublished - 1 Feb 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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