{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:18Z","timestamp":1760240058780,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,2]],"date-time":"2019-03-02T00:00:00Z","timestamp":1551484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The purpose of this paper is to represent sums of finite products of Legendre and Laguerre polynomials in terms of several orthogonal polynomials. Indeed, by explicit computations we express each of them as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, some of which involve terminating hypergeometric functions       1   F 1      and       2   F 1     .<\/jats:p>","DOI":"10.3390\/sym11030317","type":"journal-article","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T05:45:36Z","timestamp":1551678336000},"page":"317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Connection Problem for Sums of Finite Products of Legendre and Laguerre Polynomials"],"prefix":"10.3390","volume":"11","author":[{"given":"Taekyun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 01897, Korea"}]},{"given":"Kyung-Won","family":"Hwang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dong-A University, Busan 49315, Korea"}]},{"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"}]},{"given":"Dmitry V.","family":"Dolgy","sequence":"additional","affiliation":[{"name":"Institute of National Science, Far Eastern Federal University, Vladivostok 690950, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Andrews, G.E., Askey, R., and Roy, R. 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Equ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"974632","DOI":"10.1155\/2012\/974632","article-title":"Hermite polynomials and their applications associated with Bernoulli and Euler numbers","volume":"2012","author":"Kim","year":"2012","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1186\/1029-242X-2012-227","article-title":"Some identities on Bernoulli and Euler polynomials arising from orthogonality of Legendre polynomials","volume":"2012","author":"Kim","year":"2012","journal-title":"J. Inequal. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"957350","DOI":"10.1155\/2012\/957350","article-title":"Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials","volume":"2012","author":"Kim","year":"2012","journal-title":"Abstr. Appl. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"584643","DOI":"10.1155\/2012\/584643","article-title":"Some identities on Bernoulli and Hermite polynomials associated with Jacobi polynomials","volume":"2012","author":"Kim","year":"2012","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1186\/s13660-018-1744-5","article-title":"Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials","volume":"2018","author":"Kim","year":"2018","journal-title":"J. Inequal. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1186\/s13662-018-1740-6","article-title":"Sums of finite products of Legendre and Laguerre polynomials","volume":"2018","author":"Kim","year":"2018","journal-title":"Adv. Differ. Equ."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kim, T., Kim, D.S., Dolgy, D.V., and Ryoo, C.S. (2018). 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