Two-iterated degenerate Appell polynomials: properties and applications

Abstract

In the development of hybrid special polynomials, it is essential to incorporate the monomiality principle, operational rules, and other related properties. This research study adopts this approach and introduces a novel polynomial type called the two-iterated degenerate Appell polynomials, utilizing the monomiality principle. This study yields new findings that align with previous research efforts. The study presents explicit formulas and key properties of these polynomials, while also establishing connections with other polynomial types such as the Bernoulli, Euler, and Genocchi polynomials. These connections facilitate the derivation of additional results. By employing the monomiality principle and considering the aforementioned polynomials as initial members of the Appell family, this study contributes to the expansion of knowledge in the field of special polynomials.