Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q -Trigonometric Functions with Applications in Computer Modeling

Yongsheng Rao, Waseem Ahmad Khan (), Serkan Araci () and Cheon Seoung Ryoo
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Yongsheng Rao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Serkan Araci: Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep TR-27010, Turkey
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea

Mathematics, 2023, vol. 11, issue 10, 1-21

Abstract: In this article, we define q -cosine and q -sine Apostol-type Frobenius–Euler polynomials and derive interesting relations. We also obtain new properties by making use of power series expansions of q -trigonometric functions, properties of q -exponential functions, and q -analogues of the binomial theorem. By using the Mathematica program, the computational formulae and graphical representation for the aforementioned polynomials are obtained. By making use of a partial derivative operator, we derived some interesting finite combinatorial sums. Finally, we detail some special cases for these results.

Keywords: q -trigonometric functions; q -exponential functions; Frobenius–Euler polynomials; Apostol Frobenius–Euler polynomials; generating functions; combinatorial sums (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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