{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T05:20:33Z","timestamp":1783056033567,"version":"3.54.6"},"reference-count":16,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Spain Ministry of Science Innovation and Universities","doi-asserted-by":"publisher","award":["PID2021- 122154NB-I00"],"award-info":[{"award-number":["PID2021- 122154NB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Spain Ministry of Science Innovation and Universities","doi-asserted-by":"publisher","award":["PID2024-155133NB-I00"],"award-info":[{"award-number":["PID2024-155133NB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.cam.2026.117859","type":"journal-article","created":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T15:58:33Z","timestamp":1780329513000},"page":"117859","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Generalized symmetric Zernike polynomials"],"prefix":"10.1016","volume":"488","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7106-8593","authenticated-orcid":false,"given":"Misael E.","family":"Marriaga","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miguel A.","family":"Pi\u00f1ar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0001","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/1385-7258(74)90013-4","article-title":"Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators I","volume":"77","author":"Koornwinder","year":"1974","journal-title":"Indag. Math."},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0002","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/1385-7258(74)90014-6","article-title":"Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators II","volume":"77","author":"Koornwinder","year":"1974","journal-title":"Indag. Math."},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0003","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s002200050161","article-title":"The Calogero-Sutherland model and generalized classical polynomials","volume":"188","author":"Baker","year":"1997","journal-title":"Comm. Math. Phys."},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0004","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1007\/BF01193547","article-title":"Multivariate Gaussian cubature formulae","volume":"64","author":"Berens","year":"1995","journal-title":"Arch. Math. (Basel)"},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0005","first-page":"1","article-title":"Multi-dimensional Chebyshev polynomials: a non-conventional approach","volume":"10","author":"Cesarano","year":"2019","journal-title":"Commun. Appl. Ind. Math."},{"issue":"7-12","key":"10.1016\/j.cam.2026.117859_bib0006","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0031-8914(34)80259-5","article-title":"Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkon- trastmethode","volume":"1","author":"Zernike","year":"1934","journal-title":"Physica"},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0007","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.cam.2004.04.004","article-title":"Generalized Zernike or disc polynomials","volume":"174","author":"W\u00fcnsche","year":"2005","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117859_bib0008","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/j.cam.2007.12.009","article-title":"Generalized Zernike or disc polynomials: an application in quantum optics","volume":"222","author":"Torre","year":"2008","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117859_bib0009","first-page":"326","article-title":"Orthogonal polynomials in two variables","volume":"76","author":"Krall","year":"1967","journal-title":"Ann. Mat. Pure, Appl. (4)"},{"key":"10.1016\/j.cam.2026.117859_bib0010","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s40590-025-00748-2","article-title":"Ladder operators for generalized Zernike or disk polynomials","volume":"31","author":"Marriaga","year":"2025","journal-title":"Bol. Soc. Mat. Mex."},{"issue":"1","key":"10.1016\/j.cam.2026.117859_bib0011","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11075-022-01434-4","article-title":"On multivariate orthogonal polynomials and elementary symmetric functions","volume":"92","author":"Bracciali","year":"2023","journal-title":"Numer. Algo."},{"key":"10.1016\/j.cam.2026.117859_bib0012","article-title":"Orthogonal polynomials","volume":"23","author":"Szeg\u00f6","year":"1975"},{"key":"10.1016\/j.cam.2026.117859_bib0013","article-title":"Orthogonal polynomials of several variables","volume":"155","author":"Dunkl","year":"2014"},{"issue":"2","key":"10.1016\/j.cam.2026.117859_bib0014","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1080\/10652469.2014.973196","article-title":"Complex versus real orthogonal polynomials in two variables","volume":"26","author":"Xu","year":"2015","journal-title":"Integral Transforms Spec. Funct."},{"key":"10.1016\/j.cam.2026.117859_bib0015","article-title":"Algorithms in invariant theory","author":"Sturmfels","year":"2008"},{"key":"10.1016\/j.cam.2026.117859_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmaa.2025.130207","article-title":"Ladder operators for bivariate generalized classical symmetric orthogonal polynomials","volume":"555","author":"Alhama","year":"2026","journal-title":"J. Math. Anal."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005017?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005017?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T04:58:48Z","timestamp":1783054728000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":16,"alternative-id":["S0377042726005017"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117859","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Generalized symmetric Zernike polynomials","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117859","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"117859"}}