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A Note on Bell-Based Apostol-Type Frobenius-Euler Polynomials of Complex Variable with Its Certain Applications

Author

Listed:
  • Noor Alam

    (Department of Basic Sciences, Deanship of Preparatory Year, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Waseem Ahmad Khan

    (Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia)

  • Cheon Seoung Ryoo

    (Department of Mathematics, Hannam University, Daejeon 34430, Korea)

Abstract

In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties of these polynomials. We derive some explicit and implicit summation formulas and their symmetric identities by using different analytical means and applying generating functions of generalized Apostol-type Frobenius-Euler polynomials and Bell-based Apostol-type Frobenius-Euler polynomials. In particular, parametric kinds of the Bell-based Apostol-type Frobenius-Euler polynomials are introduced and some of their algebraic and analytical properties are established. In addition, illustrative examples of these families of polynomials are shown, focusing on their numerical values and piloting some beautiful computer-aided graphs of them.

Suggested Citation

  • Noor Alam & Waseem Ahmad Khan & Cheon Seoung Ryoo, 2022. "A Note on Bell-Based Apostol-Type Frobenius-Euler Polynomials of Complex Variable with Its Certain Applications," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2109-:d:841274
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    References listed on IDEAS

    as
    1. Esma Yıldız Özkan & Gözde Aksoy, 2022. "Approximation by Tensor-Product Kind Bivariate Operator of a New Generalization of Bernstein-Type Rational Functions and Its GBS Operator," Mathematics, MDPI, vol. 10(9), pages 1-13, April.
    2. Abdullah Alotaibi, 2022. "Approximation of GBS Type q -Jakimovski-Leviatan-Beta Integral Operators in Bögel Space," Mathematics, MDPI, vol. 10(5), pages 1-21, February.
    3. Sunil Kumar Sharma & Waseem A. Khan & Cheon Seoung Ryoo, 2020. "A Parametric Kind of Fubini Polynomials of a Complex Variable," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
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    Cited by:

    1. Sahar Albosaily & Waseem Ahmad Khan & Serkan Araci & Azhar Iqbal, 2022. "Fully Degenerating of Daehee Numbers and Polynomials," Mathematics, MDPI, vol. 10(14), pages 1-13, July.

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