An Algebraic Approach to the Δh-Frobenius–Genocchi–Appell Polynomials - Shahid Ahmad Wani; Sarfaraj Shaikh; Parvez Alam; Shahid Tamboli; Mohra Zayed; Javid G. Dar; Mohammad Younus Bhat (Mathematics, 2023)
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 <semantics>Δh</semantics>-Frobenius–Genocchi–Appell polynomials. The generating function of <semantics>Δh</semantics>-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 <semantics>Δh</semantics>-Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The <semantics>Δh</semantics>-Genocchi–Appell polynomials are explored as a special case and several results for <semantics>Δh</semantics>-Genocchi–Appell polynomials are also obtained.