{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T18:36:54Z","timestamp":1774636614719,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MCIN\/AEI\/10.13039\/501100011033","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}]},{"name":"MCIN\/AEI\/10.13039\/501100011033","award":["2218-122C240"],"award-info":[{"award-number":["2218-122C240"]}]},{"DOI":"10.13039\/501100004410","name":"Scientific and Technological Research Council of Turkey (TUBITAK)","doi-asserted-by":"publisher","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004410","name":"Scientific and Technological Research Council of Turkey (TUBITAK)","doi-asserted-by":"publisher","award":["2218-122C240"],"award-info":[{"award-number":["2218-122C240"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family of univariate orthogonal polynomials. For these new classes of bivariate finite orthogonal polynomials, we present a bivariate weight function, the domain of orthogonality, the orthogonality relation, the recurrence relations, the second-order partial differential equations, the generating functions, as well as the parameter derivatives. The limit relations among these families are also presented in Labelle\u2019s flavor.<\/jats:p>","DOI":"10.3390\/axioms12100932","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T07:42:08Z","timestamp":1695973328000},"page":"932","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Families of Finite Orthogonal Polynomials in Two Variables"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7653-8745","authenticated-orcid":false,"given":"Esra","family":"G\u00fcldo\u011fan Lekesiz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Gazi University, 06500 Ankara, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0872-5017","authenticated-orcid":false,"given":"Iv\u00e1n","family":"Area","sequence":"additional","affiliation":[{"name":"CITMAga, Departamento de Matem\u00e1tica Aplicada II, E.E. 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