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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yongsheng Rao & Waseem Ahmad Khan & Serkan Araci & Cheon Seoung Ryoo, 2023. "Explicit Properties of Apostol-Type Frobenius–Euler Polynomials Involving q -Trigonometric Functions with Applications in Computer Modeling," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2386-:d:1151727
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    Cited by:

    1. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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