{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T16:54:11Z","timestamp":1771692851147,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Umm Al-Qura University, Saudi Arabia","award":["25UQU4380165GSSR01"],"award-info":[{"award-number":["25UQU4380165GSSR01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A new power form representation is developed for these polynomials, which is crucial for deriving further formulas. This article also presents two connection formulas linking these generalized polynomials to the Fibonacci and Lucas polynomials, as well as several identities involving some generalized and specific Leonardo numbers. Additionally, new product formulas involving the generalized Leonardo polynomials with the Fibonacci and Lucas polynomials are provided, along with computations of definite integrals based on the derived formulas.<\/jats:p>","DOI":"10.3390\/axioms14040286","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T05:38:26Z","timestamp":1744349906000},"page":"286","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6102-671X","authenticated-orcid":false,"given":"Waleed Mohamed","family":"Abd-Elhameed","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4496-9284","authenticated-orcid":false,"given":"Omar Mazen","family":"Alqubori","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia"}]},{"given":"Abdulrahim A.","family":"Alluhaybi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0670-6712","authenticated-orcid":false,"given":"Amr Kamel","family":"Amin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"ref_1","first-page":"7","article-title":"The Fibonacci numbers and its amazing applications","volume":"6","author":"Sinha","year":"2017","journal-title":"Int. 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