Advances in Difference Equations | |
Construction of the type 2 poly-Frobenius–Genocchi polynomials with their certain applications | |
article | |
Duran, Ugur1  Acikgoz, Mehmet2  Araci, Serkan3  | |
[1] Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Tecnical University;Department of Mathematics, Faculty of Arts and Science, University of Gaziantep;Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University | |
关键词: Polylogarithm function; Polyexponential function; Frobenius–Genocchi polynomials; Poly-Frobenius–Genocchi polynomials; | |
DOI : 10.1186/s13662-020-02889-2 | |
学科分类:航空航天科学 | |
来源: SpringerOpen | |
【 摘 要 】
Kim and Kim (Russ. J. Math. Phys. 26(1):40–49, 2019) have studied the type 2 poly-Bernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius–Genocchi polynomials, which is called the type 2 poly-Frobenius–Genocchi polynomials, by means of the polyexponential function. We also derive some new relations and properties including the Stirling numbers of the first and second kinds. In a special case, we give a relation between the type 2 poly-Frobenius–Genocchi polynomials and Bernoulli polynomials of order k. Moreover, motivated by the definition of the unipoly-Bernoulli polynomials given in (Kim and Kim in Russ. J. Math. Phys. 26(1):40–49, 2019), we introduce the unipoly-Frobenius–Genocchi polynomials via a unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Frobenius–Genocchi polynomials and the classical Frobenius–Genocchi polynomials.
【 授权许可】
CC BY
【 预 览 】
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