Abstract
A fresh class of hybrid special polynomials, termed the Bell-enriched Appell-lambda-polynomials, is constructed through the discrete convolution of Bell-based lambda-polynomials with the Appell sequence. A generating function for this class is established, from which closed-form expansions, convolution identities, and Stirling-number factorizations follow. The multiplicative and derivative operators that give this family its quasi-monomial character are identified, and the associated differential equation is recorded as an immediate corollary. A determinant representation `a la Wang is also obtained. To illustrate the scope of the general theory, three subfamilies are investigated: the Bell-enriched Bernoulli-lambda and Euler-lambda polynomials, which are admissible Appell specializations (mathcal{A}(0) neq 0), and the Bell-enriched Genocchi-lambda polynomials, which belong to the associated-Appell class (mathcal{A}(0)=0) and are treated separately. For the first two subfamilies, operational, quasi-monomial, and determinantal properties are fully established; for the Genocchi subfamily, generating-function and operational results are obtained within the associated-Appell framework. A numerical exploration of polynomial values, zero distributions, and graphical profiles supplements the algebraic development.