On Generalized Lagrange-Based Apostol-type and Related Polynomials

In this article, we introduce a new class of generalized polynomials, ascribed to the new families of generating functions and identities concerning Lagrange, Hermite, Miller-Lee, and Laguerre polynomials and of their associated forms. It is shown that the proposed method allows the derivation of sum rules involving products of generalized polynomials and addition theorems. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. The possibility of extending the results to include generating functions involving products of Lagrange-based unified Apostol-type and other polynomials is finally analyzed.