Introducing Δ h Hermite-based Appell polynomials via the monomiality principle: properties, forms, and generating relations

Abstract

The article introduces a novel class of polynomials, H Qm (q 1 , q 2 , q 3 , q 4 , q 5 ; h), termed ∆ h Hermite-based Appell polynomials, utilizing the monomiality principle. These polynomials exhibit close connections with ∆ h Hermite-based Bernoulli, Euler, and Genocchi polynomials, elucidating their specific properties and explicit forms. Moreover, the research establishes generating relations for these polynomials, facilitating profound insights applicable across diverse domains such as mathematics, physics, and engineering sciences.