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Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

Author

Listed:
  • Yuan He

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, Yunnan, China)

  • Serkan Araci

    (Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

  • Mahmoud Abdel-Aty

    (Zewail City of Science andTechnology, University of Science and Technology, Cairo 82524, Egypt)

Abstract

In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. Some results presented here are the corresponding extensions of several known formulas.

Suggested Citation

  • Yuan He & Serkan Araci & Hari M. Srivastava & Mahmoud Abdel-Aty, 2018. "Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials," Mathematics, MDPI, vol. 6(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:329-:d:190657
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    References listed on IDEAS

    as
    1. Luo, Qiu-Ming, 2015. "Elliptic extensions of the Apostol–Bernoulli and Apostol–Euler polynomials," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 156-166.
    2. He, Yuan & Kim, Taekyun, 2018. "A higher-order convolution for Bernoulli polynomials of the second kind," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 51-58.
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    Cited by:

    1. Monairah Alansari & Mumtaz Riyasat & Subuhi Khan & Kaleem Raza Kazmi, 2019. "Finding Determinant Forms of Certain Hybrid Sheffer Sequences," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    2. Paolo Emilio Ricci & Rekha Srivastava & Diego Caratelli, 2024. "Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials," Mathematics, MDPI, vol. 12(3), pages 1-16, January.

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