{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T18:25:52Z","timestamp":1767205552310,"version":"build-2238731810"},"reference-count":11,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:00:00Z","timestamp":1596412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PGC2018\u2013096504-B-C33"],"award-info":[{"award-number":["PGC2018\u2013096504-B-C33"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey\u2013Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy.<\/jats:p>","DOI":"10.3390\/sym12081290","type":"journal-article","created":{"date-parts":[[2020,8,4]],"date-time":"2020-08-04T05:56:46Z","timestamp":1596520606000},"page":"1290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Terminating Basic Hypergeometric Representations and Transformations for the Askey\u2013Wilson Polynomials"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9398-455X","authenticated-orcid":false,"given":"Howard S.","family":"Cohl","sequence":"first","affiliation":[{"name":"Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9545-7411","authenticated-orcid":false,"given":"Roberto S.","family":"Costas-Santos","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}]},{"given":"Linus","family":"Ge","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Rochester, Rochester, NY 14627, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Koekoek, R., Lesky, P.A., and Swarttouw, R.F. (2010). Hypergeometric Orthogonal Polynomials and Their q-Analogues, Springer-Verlag. Springer Monographs in Mathematics.","DOI":"10.1007\/978-3-642-05014-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s11139-006-0245-1","article-title":"An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)","volume":"13","author":"Rosengren","year":"2007","journal-title":"Ramanujan J."},{"key":"ref_3","unstructured":"Ismail, M.E.H., and Zhang, R. (2020). New Orthogonal Polynomials of Askey-Wilson Type, in preparation."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6692","DOI":"10.1063\/1.533115","article-title":"Invariance groups of transformations of basic hypergeometric series","volume":"40","author":"Rao","year":"1999","journal-title":"J. Math. Phys."},{"key":"ref_5","unstructured":"Krattenthaler, C., and Rao, S.K. (2004). On group theoretical aspects, hypergeometric transformations and symmetries of angular momentum coefficients. Symmetries in Science XI, Kluwer Academic Publishers."},{"key":"ref_6","first-page":"026","article-title":"Symmetry groups of An hypergeometric series","volume":"10","author":"Kajihara","year":"2014","journal-title":"SIGMA. Symmetry Integr. Geom."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Gasper, G., and Rahman, M. (2004). Basic Hypergeometric Series, Cambridge University Press. [2nd ed.]. Encyclopedia of Mathematics and Its Applications.","DOI":"10.1017\/CBO9780511526251"},{"key":"ref_8","unstructured":"Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V., Cohl, H.S., and McClain, M.A. (2020, June 09). NIST Digital Library of Mathematical Functions, Available online: http:\/\/dlmf.nist.gov\/."},{"key":"ref_9","unstructured":"Koornwinder, T.H. (2015). Additions to the formula lists in \u201cHypergeometric orthogonal polynomials and their q-analogues\u201d by Koekoek, Lesky and Swarttouw. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0021-9045(82)90069-7","article-title":"Asymptotic and generating relations for the q-Jacobi and 4\u03c63 polynomials","volume":"36","author":"Ismail","year":"1982","journal-title":"J. Approx. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Askey, R., and Wilson, J. (1985). Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Am. Math. Soc., 54.","DOI":"10.1090\/memo\/0319"}],"updated-by":[{"DOI":"10.3390\/sym12122120","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:00:00Z","timestamp":1596412800000}}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1290\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T22:48:30Z","timestamp":1754261310000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1290"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,3]]},"references-count":11,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["sym12081290"],"URL":"https:\/\/doi.org\/10.3390\/sym12081290","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,3]]}}}