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


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
Issue number2
Publication statusPublished - 1 Feb 2020


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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