Exploration of k-hypergeometric polynomials and their mathematical implications

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dc.contributor.authorOzmen, Nejla
dc.contributor.authorCin, Yahya
dc.date.accessioned2026-07-01T11:39:28Z
dc.date.available2026-07-01T11:39:28Z
dc.date.issued2025
dc.departmentDüzce Üniversitesi
dc.description.abstractIn current study, we focus on a mathematical concept called the k-hypergeometric polynomials. These polynomials are constructed using a mathematical tool called the Pochhammer k-symbol, as introduced by [R. Diaz, E. Pariguan, On hypergeometric functions and pochhammer k-symbol, Divulg. Mat. 15(2007), 179-192]. We develop several theorems related to these k-hypergeometric polynomials. Using these theorems, we derive two important functions: a multilinear generating function and a multilateral generating function for k-hypergeometric polynomials. These functions play a crucial role in our analysis. Furthermore, extend our research to explore the concept of the k-fractional secondary driver. This extension is based on the properties of k-hypergeometric polynomials and another mathematical entity known as the beta k-function. To make these connections, we utilize the Riemann-Liouville k-fractional process, as described by [G. Rahman, S. Nisar Mubeen, K. Sooppy, On generalized k-fractional derivative operator, AIMS Math. 5(2020), 1936-1945]. This has allowed us to establish some novel results, which are analogous to well-known mathematical transformations like the Mellin transformation. Additionally, we explore the relationships between our findings and other mathematical functions, such as hypergeometric and Appell' k-functions. In the last section of our paper, we delve into the relationship between k-hypergeometric polynomials and two specific mathematical functions: We also provide an integral representation of k-hypergeometric polynomials. Overall, our research paper contributes to the understanding of k-hypergeometric polynomials and their connections to various mathematical functions and transformations.
dc.identifier.doi10.2298/FIL2526329O
dc.identifier.endpage9345
dc.identifier.issn0354-5180
dc.identifier.issue26
dc.identifier.scopus2-s2.0-105022910557
dc.identifier.scopusqualityQ2
dc.identifier.startpage9329
dc.identifier.urihttps://doi.org/10.2298/FIL2526329O
dc.identifier.urihttps://hdl.handle.net/20.500.12684/23308
dc.identifier.volume39
dc.identifier.wosWOS:001629622000001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherUniv Nis, Fac Sci Math
dc.relation.ispartofFilomat
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20260623
dc.subject. Gamma And Beta K-Function
dc.subjectK-Hypergeometric Polynomials
dc.subjectGenerating Function
dc.subjectMultilinear And Multilateral Gener-Ating Functions
dc.subjectFractional Derivative Operators
dc.subjectIntegral Representation
dc.titleExploration of k-hypergeometric polynomials and their mathematical implications
dc.typeArticle

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