{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:43:38Z","timestamp":1760237018578,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T00:00:00Z","timestamp":1581638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad de Monterrey","award":["UIN19562"],"award-info":[{"award-number":["UIN19562"]}]},{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["287523"],"award-info":[{"award-number":["287523"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006302","name":"Universidad de Alcal\u00e1","doi-asserted-by":"publisher","award":["CM\/JIN\/2019-010"],"award-info":[{"award-number":["CM\/JIN\/2019-010"]}],"id":[{"id":"10.13039\/501100006302","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/math8020246","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T10:10:25Z","timestamp":1582020625000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2755-0235","authenticated-orcid":false,"given":"Lino G.","family":"Garza","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Monterrey, San Pedro Garza Garc\u00eda, Nuevo Le\u00f3n 66238, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2569-186X","authenticated-orcid":false,"given":"Luis E.","family":"Garza","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6802-3303","authenticated-orcid":false,"given":"Edmundo J.","family":"Huertas","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, Alcal\u00e1 de Henares, Madrid 28801, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,14]]},"reference":[{"key":"ref_1","first-page":"245","article-title":"On some properties of certain solutions of a differential equation of the second-order","volume":"16","author":"Routh","year":"1885","journal-title":"Proc. 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