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An Algebraic Approach to the Δ h -Frobenius–Genocchi–Appell Polynomials

Author

Listed:
  • Shahid Ahmad Wani

    (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, India)

  • Sarfaraj Shaikh

    (Department Mechanical Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, India)

  • Parvez Alam

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 600127, India)

  • Shahid Tamboli

    (Department Mechanical Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, India)

  • Mohra Zayed

    (Mathematics Department, College of Science, King Khalid University, Abha 61421, Saudi Arabia)

  • Javid G. Dar

    (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, India)

  • Mohammad Younus Bhat

    (Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India)

Abstract

In recent years, the generating function of mixed-type special polynomials has received growing interest in several fields of applied sciences and physics. This article intends to study a new class of polynomials, called the Δ h -Frobenius–Genocchi–Appell polynomials. The generating function of Δ h -Frobenius–Genocchi–Appell polynomials is constructed and some of their fundamental properties are studied. By making use of this generating function, we investigate some novel and interesting results, such as recurrence relations, explicit representations, and implicit formulas for the Δ h -Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The Δ h -Genocchi–Appell polynomials are explored as a special case and several results for Δ h -Genocchi–Appell polynomials are also obtained.

Suggested Citation

  • Shahid Ahmad Wani & Sarfaraj Shaikh & Parvez Alam & Shahid Tamboli & Mohra Zayed & Javid G. Dar & Mohammad Younus Bhat, 2023. "An Algebraic Approach to the Δ h -Frobenius–Genocchi–Appell Polynomials," Mathematics, MDPI, vol. 11(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2029-:d:1132045
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    References listed on IDEAS

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    1. Taekyun Kim & Byungje Lee, 2009. "Some Identities of the Frobenius-Euler Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-7, March.
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