{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:13Z","timestamp":1760239633770,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education","award":["NRF-2020R111A1A01052440"],"award-info":[{"award-number":["NRF-2020R111A1A01052440"]}]},{"name":"Government of India","award":["MTR\/2017\/000821"],"award-info":[{"award-number":["MTR\/2017\/000821"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A remarkably large of number of polynomials have been presented and studied. Among several important polynomials, Legendre polynomials, Gould-Hopper polynomials, and Sheffer polynomials have been intensively investigated. In this paper, we aim to incorporate the above-referred three polynomials to introduce the Legendre-Gould Hopper-based Sheffer polynomials by modifying the classical generating function of the Sheffer polynomials. In addition, we investigate diverse properties and formulas for these newly introduced polynomials.<\/jats:p>","DOI":"10.3390\/sym12122051","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T22:15:36Z","timestamp":1607638536000},"page":"2051","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods"],"prefix":"10.3390","volume":"12","author":[{"given":"Nabiullah","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohd","family":"Aman","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Talha","family":"Usman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Basic and Applied Sciences, Lingaya\u2019s Vidyapeeth, Faridabad 121002, Haryana, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7240-7737","authenticated-orcid":false,"given":"Junesang","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dongguk University, Gyeongju 38066, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2169","DOI":"10.1016\/j.amc.2010.07.016","article-title":"Some properties of Hermite-based Sheffer polynomials","volume":"217","author":"Khan","year":"2010","journal-title":"Appl. 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