@article{b5c01f6a94324c86b0253efadcfdb17f,
title = "On differential equations associated with perturbations of orthogonal polynomials on the unit circle",
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.",
author = "Garza, {Lino G.} and Garza, {Luis E.} and Huertas, {Edmundo J.}",
note = "Funding Information: The work of the first author was supported by Universidad de Monterrey under grant UIN19562. The work of the second author was supported by M?xico's Conacyt Grant 287523. The work of the third author (EJH) was supported by Direcci?n General de Investigaci?n e Innovaci?n, Consejer?a de Educaci?n e Investigaci?n of the Comunidad de Madrid (Spain), and Universidad de Alcal? under grant CM/JIN/2019-010, (Proyectos de I+D Para J?venes Investigadores de la Universidad de Alcal? 2019). We thank the anonymous referees for carefully reviewing our manuscript. Their valuable comments have substantially improved our work. Funding Information: Funding: The work of the first author was supported by Universidad de Monterrey under grant UIN19562. The work of the second author was supported by M{\'e}xico{\textquoteright}s Conacyt Grant 287523. The work of the third author (EJH) was supported by Direcci{\'o}n General de Investigaci{\'o}n e Innovaci{\'o}n, Consejer{\'i}a de Educaci{\'o}n e Investigaci{\'o}n of the Comunidad de Madrid (Spain), and Universidad de Alcal{\'a} under grant CM/JIN/2019-010, (Proyectos de I+D Para J{\'o}venes Investigadores de la Universidad de Alcal{\'a} 2019). Publisher Copyright: {\textcopyright} 2020 by the authors. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = feb,
day = "1",
doi = "10.3390/math8020246",
language = "English",
volume = "8",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "2",
}