Certain Properties and Characterizations of ∆_h-Truncated Exponential Based Hermite Polynomials

This article introduces a novel class of ∆_h-truncated exponential-based Hermite polynomials and examine their fundamental properties and structural identities. We derive generating functions, recurrence relations, and explicit formulas, along with summation identities. The study further uncovers connections with the monomiality principle, offering insights into their underlying algebraic framework. In addition, an operational formalism is developed, and symmetric identities are established to enhance the theoretical foundation of these polynomials.