@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: 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",

}