Analytical properties of type 2 degenerate poly-Bernoulli polynomials associated with their applications
| Autor: | Abdulghani Muhyi, Ghulam Muhiuddin, Deena Al-Kadi, Waseem A. Khan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Partial differential equation Modified degenerate polyexponential functions Applied Mathematics Degenerate energy levels Function (mathematics) Type (model theory) Bernoulli polynomials Type 2 degenerate central Bell polynomials symbols.namesake Ordinary differential equation symbols QA1-939 Arithmetic function Type 2 degenerate Bernoulli polynomials Analysis Mathematics Unipoly functions |
| Zdroj: | Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-18 (2021) |
| ISSN: | 1687-1847 |
| Popis: | Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we investigate the degenerate type 2 poly-Bernoulli numbers and polynomials which are derived from the moderated version of degenerate polyexponential functions. Our degenerate type 2 degenerate poly-Bernoulli numbers and polynomials are different from those of Kim et al. (Adv. Differ. Equ. 2020:168, 2020) and Kim and Kim (Russ. J. Math. Phys. 26(1):40–49, 2019). Utilizing the properties of moderated degenerate poly-exponential function, we explore some properties of our type 2 degenerate poly-Bernoulli numbers and polynomials. From our investigation, we derive some explicit expressions for type 2 degenerate poly-Bernoulli numbers and polynomials. In addition, we also scrutinize type 2 degenerate unipoly-Bernoulli polynomials related to an arithmetic function and investigate some identities for those polynomials. In particular, we consider certain new explicit expressions and relations of type 2 degenerate unipoly-Bernoulli polynomials and numbers related to special numbers and polynomials. Further, some related beautiful zeros and graphical representations are displayed with the help of Mathematica. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|