{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:31:03Z","timestamp":1772253063620,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T00:00:00Z","timestamp":1541721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2017R1E1A1A03070882"],"award-info":[{"award-number":["2017R1E1A1A03070882"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper treats the connection problem of expressing sums of finite products of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal polynomials. In fact, by carrying out explicit computations each of them are expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials which involve some terminating hypergeometric functions      F 0 2  ,  F 1 2     , and      F 2 3     .<\/jats:p>","DOI":"10.3390\/sym10110617","type":"journal-article","created":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T03:27:31Z","timestamp":1542079651000},"page":"617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds"],"prefix":"10.3390","volume":"10","author":[{"given":"Dmitry Victorovich","family":"Dolgy","sequence":"first","affiliation":[{"name":"Institute of National Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-7015","authenticated-orcid":false,"given":"Dae San","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sogang University, Seoul 04107, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taekyun","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China"},{"name":"Department of Mathematics, Kwangwoon University, Seoul 01897, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jongkyum","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Gyeongsangnamdo, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,9]]},"reference":[{"key":"ref_1","first-page":"361","article-title":"Identities involving Bernoulli and Euler polynomials arising from Chebyshev polynomials","volume":"15","author":"Kim","year":"2012","journal-title":"Proc. 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