{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:24Z","timestamp":1760234064182,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"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":["Symmetry"],"abstract":"<jats:p>In this contribution we obtain some algebraic properties associated with the sequence of polynomials orthogonal with respect to the Sobolev-type inner product:p,qs=\u222bRp(x)q(x)d\u03bc(x)+M0p(0)q(0)+M1p\u2032(0)q\u2032(0), where p,q are polynomials, M0, M1 are non-negative real numbers and \u03bc is a symmetric positive measure. These include a five-term recurrence relation, a three-term recurrence relation with rational coefficients, and an explicit expression for its norms. Moreover, we use these results to deduce asymptotic properties for the recurrence coefficients and a nonlinear difference equation that they satisfy, in the particular case when d\u03bc(x)=e\u2212x4dx.<\/jats:p>","DOI":"10.3390\/sym13040534","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T21:09:45Z","timestamp":1616706585000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Analysis of the Recurrence Coefficients for Symmetric Sobolev-Type Orthogonal Polynomials"],"prefix":"10.3390","volume":"13","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, Ctra. Madrid-Barcelona, Km. 33,600, Facultad de Ciencias, 28805 Alcal\u00e1 de Henares, Madrid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1111\/sapm.12105","article-title":"A generalized Freud weight","volume":"136","author":"Clarkson","year":"2016","journal-title":"Stud. Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jat.2017.10.001","article-title":"Properties of generalized Freud polynomials","volume":"225","author":"Clarkson","year":"2018","journal-title":"J. Approx. 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