An Algebraic Approach to the Δ<i>_h</i>-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 Δh-Frobenius–Genocchi–Appell polynomials. The generating function of Δh-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 Δh-Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The Δh-Genocchi–Appell polynomials are explored as a special case and several results for Δh-Genocchi–Appell polynomials are also obtained.

Keywords

• Frobenius–Genocchi polynomials
• Δ<i>_h</i>–Appell polynomials
• quasi-monomiality
• determinant form