{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T10:04:50Z","timestamp":1771668290541,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,11]],"date-time":"2021-04-11T00:00:00Z","timestamp":1618099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006261","name":"Taif University","doi-asserted-by":"publisher","award":["TURSP-2020\/246"],"award-info":[{"award-number":["TURSP-2020\/246"]}],"id":[{"id":"10.13039\/501100006261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange\u2013Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller\u2013Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite\u2013Miller\u2013Lee polynomials.<\/jats:p>","DOI":"10.3390\/sym13040648","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T21:47:33Z","timestamp":1618264053000},"page":"648","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange\u2013Hermite Polynomials"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5717-1199","authenticated-orcid":false,"given":"Ugur","family":"Duran","sequence":"additional","affiliation":[{"name":"Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, TR-31200 Hatay, Turkey"}]},{"given":"Deena","family":"Al-Kadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/10652460500432006","article-title":"On a multi-variable extension of the Lagrange-Hermite polynomials","volume":"17","author":"Altin","year":"2006","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/10652460108819340","article-title":"The Lagrange Polynomials in Several Variables","volume":"12","author":"Chan","year":"2001","journal-title":"Int. Trans. Spec. Func."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/1065246031000098186","article-title":"The Lagrange polynomials the associated generalizations, and the umbral calculus","volume":"14","author":"Dattoil","year":"2003","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_4","first-page":"19","article-title":"Integral representations of new families of polynomials","volume":"15","author":"Dattoli","year":"2004","journal-title":"Ital. J. Pure Appl. Math."},{"key":"ref_5","unstructured":"Dilcher, K. (2002). Bernoulli numbers and confluent hypergeometric functions. 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Hungar."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hu, S., and Komatsu, T. (2019). Explicit expressions for the related numbers of higher-order Appell polynomials. Quaest. Math., 1\u201311.","DOI":"10.2989\/16073606.2019.1596174"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Iwasawa, K. (1972). Lectures on p-adic L-Functions, Princeton University Press.","DOI":"10.1515\/9781400881703"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1142\/S1793042111005027","article-title":"A p-adic view of multiple sums of powers","volume":"7","author":"Kim","year":"2011","journal-title":"Int. J. Number Theory"},{"key":"ref_13","unstructured":"N\u00f6rlund, M.E. (1924). Differenzenrechnung, Springer-Verlag."},{"key":"ref_14","unstructured":"Srivastava, H.M., and Manocha, H.L. (1984). A Treatise on Generating Functions, Ellis Horwood Limited. Co."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/648\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:59:27Z","timestamp":1760363967000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/4\/648"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,11]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["sym13040648"],"URL":"https:\/\/doi.org\/10.3390\/sym13040648","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,11]]}}}