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Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

Author

Listed:
  • Talha Usman

    (Department of General Requirements, University of Technology and Applied Sciences-Sur, Sur 411, Oman)

  • Nabiullah Khan

    (Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India)

  • Mohd Aman

    (Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India)

  • Shrideh Al-Omari

    (Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Junesang Choi

    (Department of Mathematics, Dongguk University, Gyeongju 38066, Korea)

Abstract

Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee polynomials and to explore some of their features and identities. We investigate these polynomials via generating functions and deduce various identities, summation formulae, differential and integral formulas, implicit summation formulae, and several characterized generating functions for new numbers and polynomials. Finally, by using an operational version of Apostol–Genocchi polynomials, we derive some results in terms of new special polynomials. Due to the generic nature of the findings described here, they are used to reduce and generate certain known or novel formulae and identities for relatively simple polynomials and numbers.

Suggested Citation

  • Talha Usman & Nabiullah Khan & Mohd Aman & Shrideh Al-Omari & Kamsing Nonlaopon & Junesang Choi, 2022. "Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2502-:d:865547
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    Cited by:

    1. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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