Exploration of k-hypergeometric polynomials and their mathematical implications
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
. Gamma And Beta K-Function, K-Hypergeometric Polynomials, Generating Function, Multilinear And Multilateral Gener-Ating Functions, Fractional Derivative Operators, Integral Representation
Kaynak
Filomat
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
39
Sayı
26
