Construction of the type 2 poly-Frobenius–Genocchi polynomials with their certain applications

Advances in Difference Equations

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