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We\u00a0deduce properties for the recurrence relation coefficients from differential properties of the weight. We take the so called generalized modified Jacobi and Bessel weights as a case\u00a0study.<\/jats:p>","DOI":"10.1007\/s11075-025-02197-4","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T09:40:19Z","timestamp":1754559619000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized semiclassical orthogonal polynomials on the unit\u00a0circle: A Riemann\u2013Hilbert perspective"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4685-1583","authenticated-orcid":false,"given":"Am\u00edlcar","family":"Branquinho","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5097-950X","authenticated-orcid":false,"given":"Ana","family":"Foulqui\u00e9-Moreno","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8015-0070","authenticated-orcid":false,"given":"Karina","family":"Rampazzi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"2197_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791246","volume-title":"Complex Variables: Introduction and Applications","author":"M Ablowitz","year":"2003","unstructured":"Ablowitz, M., Fokas, A.: Complex Variables: Introduction and Applications. 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