An Algebraic Approach to the Δh-Frobenius–Genocchi–Appell Polynomials

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 (Formula presented.) -Frobenius–Genocchi–Appell polynomials. The generating function of (Formula presented.) -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 (Formula presented.) -Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The (Formula presented.) -Genocchi–Appell polynomials are explored as a special case and several results for (Formula presented.) -Genocchi–Appell polynomials are also obtained.