Abstract
The development of certain aspects of special polynomials in line with the monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research. By using the monomiality principle, new outcomes are produced, and their differential equation and series representation is obtained, which are important in several branches of mathematics and physics. Thus, in line with prior facts, our aim is to introduce the Delta(h) hybrid special polynomials associated with Hermite polynomials denoted by (Delta hH)Q(m)(u, v, w; h). Further, we obtain some well-known main properties and explicit forms satisfied by these polynomials.