{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T10:21:16Z","timestamp":1770891676293,"version":"3.50.1"},"reference-count":19,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004761","name":"Hainan Provincial Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2019RC199"],"award-info":[{"award-number":["2019RC199"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hainan Provincial Education and Teaching Reform Project of Colleges and Universities","award":["Hnjg2019-46"],"award-info":[{"award-number":["Hnjg2019-46"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62167003"],"award-info":[{"award-number":["62167003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2023]]},"DOI":"10.1109\/access.2023.3283028","type":"journal-article","created":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T17:56:26Z","timestamp":1685987786000},"page":"56481-56493","source":"Crossref","is-referenced-by-count":2,"title":["An Automatic Method for Generating Symbolic Expressions of Zernike Circular Polynomials"],"prefix":"10.1109","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4400-9133","authenticated-orcid":false,"given":"Hong-Yan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Hainan Normal University, Haikou, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8481-1796","authenticated-orcid":false,"given":"Yu","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Hainan Normal University, Haikou, China"}]},{"given":"Fu-Yun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Hainan Normal University, Haikou, China"}]}],"member":"263","reference":[{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1080\/713819334"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-3203(02)00091-2"},{"key":"ref15","author":"knuth","year":"1997","journal-title":"The Art of Computer Programming Volume 1 Fundamental Algorithms"},{"key":"ref14","article-title":"Balanced binary tree schemes for computing Zernike radial polynomials","author":"zhang","year":"2022","journal-title":"arXiv 2212 02495"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.66.000207"},{"key":"ref10","year":"2008","journal-title":"EMAX Optical Design Program User&#x2019;s Guide"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.71.000075"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139644181"},{"key":"ref17","author":"zhang","year":"1996","journal-title":"Computation of Special Functions"},{"key":"ref16","author":"graham","year":"1994","journal-title":"Concrete Mathematics A Foundation for Computer Science"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1117\/3.927341"},{"key":"ref18","author":"wyant","year":"2022","journal-title":"Zernike Polynomial"},{"key":"ref8","author":"berger","year":"2022","journal-title":"Zernike Aberrations"},{"key":"ref7","first-page":"1945","author":"b\u00fchren","year":"2018","journal-title":"Zernike Coefficients"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1002\/9780470135976"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1364\/OL.38.002487"},{"key":"ref3","article-title":"Zernike circle polynomials and infinite integrals involving the product of Bessel functions","author":"janssen","year":"2010","journal-title":"arXiv 1007 0667"},{"key":"ref6","article-title":"Zernike basis to Cartesian transformations","author":"mathar","year":"2008","journal-title":"arXiv 0809 2368"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1364\/AO.52.001136"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/6287639\/10005208\/10144301.pdf?arnumber=10144301","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T18:21:39Z","timestamp":1688408499000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10144301\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":19,"URL":"https:\/\/doi.org\/10.1109\/access.2023.3283028","relation":{},"ISSN":["2169-3536"],"issn-type":[{"value":"2169-3536","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]}}}