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

Shahid Ahmad Wani, Sarfaraj Shaikh, Parvez Alam, Shahid Tamboli, Mohra Zayed, Javid G. Dar and Mohammad Younus Bhat ()
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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

Mathematics, 2023, vol. 11, issue 9, 1-13

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.

Keywords: Frobenius–Genocchi polynomials; ? h –Appell polynomials; quasi-monomiality; determinant form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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