{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:46:08Z","timestamp":1765039568899,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T00:00:00Z","timestamp":1608595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002468","name":"Dong-A university","doi-asserted-by":"publisher","award":["Dong-A university"],"award-info":[{"award-number":["Dong-A university"]}],"id":[{"id":"10.13039\/501100002468","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We get the 3-variable degenerate Hermite Kamp\u00e9 de F\u00e9riet polynomials and get symmetric identities for 3-variable degenerate Hermite Kamp\u00e9 de F\u00e9riet polynomials. We make differential equations coming from the generating functions of degenerate Hermite Kamp\u00e9 de F\u00e9riet polynomials to get some identities for 3-variable degenerate Hermite Kamp\u00e9 de F\u00e9riet polynomials,. Finally, we study the structure and symmetry of pattern about the zeros of the 3-variable degenerate Hermite Kamp\u00e9 de F\u00e9riet equations.<\/jats:p>","DOI":"10.3390\/sym13010007","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T20:39:29Z","timestamp":1608669569000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Explicit Identities for 3-Variable Degenerate Hermite Kamp\u00e9 de F\u00e9riet Polynomials and Differential Equation Derived from Generating Function"],"prefix":"10.3390","volume":"13","author":[{"given":"Kyung-Won","family":"Hwang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dong-A University, Busan 49315, Korea"}]},{"given":"Young-Soo","family":"Seol","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dong-A University, Busan 49315, Korea"}]},{"given":"Cheon-Seoung","family":"Ryoo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hannam University, Daejeon 34430, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,22]]},"reference":[{"key":"ref_1","unstructured":"Andrews, L.C. (1985). Special Functions for Engineers and Mathematicians, Macmillan. Co."},{"key":"ref_2","unstructured":"Appell, P., and de F\u00e9riet, J.H.K. (1926). Fonctions Hyperg\u00e9om\u00e9triques et Hypersph\u00e9riques: Polynomes d Hermite, Gauthier-Villars."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0377-0427(00)00283-1","article-title":"Generalized Polynomials Operational Identities and Their Applications","volume":"118","author":"Dattoli","year":"2000","journal-title":"J. Comput. Appl. Math."},{"key":"ref_4","unstructured":"Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1981). Higher Transcendental Functions, Krieger."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Andrews, G.E., Askey, R., and Roy, R. (1999). Special Functions, Cambridge University Press.","DOI":"10.1017\/CBO9781107325937"},{"key":"ref_6","unstructured":"Arfken, G. (1985). Mathematical Methods for Physicists, Academic Press. [3rd ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1016\/j.jmaa.2008.11.002","article-title":"Hermite-based Appell polynomials: Properties and applications","volume":"351","author":"Khan","year":"2009","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","first-page":"51","article-title":"Degenerate Stiling, Bernoulli and Eulerian numbers","volume":"15","author":"Carlitz","year":"1979","journal-title":"Utilitas Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.jnt.2007.02.007","article-title":"Degenerate Bernoulli polynomials, generalized factorial sums, and their applications","volume":"128","author":"Young","year":"2008","journal-title":"J. Number Theorey"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1016\/j.disc.2006.10.013","article-title":"Notes on degenerate numbers","volume":"307","author":"Cenkci","year":"2007","journal-title":"Discrete Math."},{"key":"ref_11","first-page":"3631","article-title":"Notes on degenerate tangent polynomials","volume":"11","author":"Ryoo","year":"2015","journal-title":"Glob. J. Pure Appl. Math."},{"key":"ref_12","first-page":"651","article-title":"Degenerate Bernoulli numbers and polynomials associated with degenerate Hermite polynomials","volume":"33","author":"Haroon","year":"2018","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hwang, K.W., and Ryoo, C.S. (2020). Some identities involving two-variable partially degenerate Hermite polynomials induced from differential equations and structure of their roots. Mathematics, 8.","DOI":"10.3390\/math8040632"},{"key":"ref_14","first-page":"453","article-title":"Differential equations associated with Mahler and Sheffer-Mahler polynomials","volume":"24","author":"Kim","year":"2019","journal-title":"Nonlinear Funct. Anal. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4474","DOI":"10.22436\/jnsa.010.08.39","article-title":"A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials","volume":"10","author":"Ryoo","year":"2017","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"487","DOI":"10.14317\/jami.2016.487","article-title":"Differential equations associated with tangent numbers","volume":"34","author":"Ryoo","year":"2016","journal-title":"J. Appl. Math. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ryoo, C.S. (2019). Some identities involving Hermitt Kamp\u00e9 de F\u00e9riet polynomials arising from differential equations and location of their zeros. Mathematics, 7.","DOI":"10.3390\/math7010023"},{"key":"ref_18","first-page":"453","article-title":"Differential equations associated with Bell-Carlitz polynomials and their zeros","volume":"24","author":"Ryoo","year":"2016","journal-title":"Neural Parallel Sci. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:48:33Z","timestamp":1760179713000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,22]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010007"],"URL":"https:\/\/doi.org\/10.3390\/sym13010007","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,22]]}}}