{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:39:19Z","timestamp":1760146759538,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,7]],"date-time":"2024-12-07T00:00:00Z","timestamp":1733529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper explores the operational principles and monomiality principles that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining consistent with established findings. The primary focus of this study is the introduction of degenerate multidimensional Hermite-based Appell polynomials (DMHAP), denoted as An[r]H(l1,l2,l3,\u2026,lr;\u03d1). These DMHAP forms essential families of orthogonal polynomials, demonstrating strong connections with classical Hermite and Appell polynomials. Additionally, we derive symmetric identities and examine the fundamental properties of these polynomials. Finally, we establish an operational framework to investigate and develop these polynomials further.<\/jats:p>","DOI":"10.3390\/axioms13120859","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T11:16:48Z","timestamp":1733743008000},"page":"859","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Awatif Muflih","family":"Alqahtani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shaqra University, Riyadh 11972, Saudi Arabia"}]},{"given":"Saleem","family":"Yousuf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Srinagar 190006, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6484-469X","authenticated-orcid":false,"given":"Shahid Ahmad","family":"Wani","sequence":"additional","affiliation":[{"name":"Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9545-7411","authenticated-orcid":false,"given":"Roberto S.","family":"Costas-Santos","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, Universidad Loyola Andaluc\u00eda, 41704 Seville, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"119","DOI":"10.24033\/asens.186","article-title":"Sur une classe de polyn\u00f4mes","volume":"9","author":"Appell","year":"1880","journal-title":"Ann. 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