SOME NEW CLASSES OF GENERALIZED LAGRANGE-BASED APOSTOL TYPE HERMITE POLYNOMIALS

In this paper, we present a general family of Lagrange-based Apostol- type Hermite polynomials thereby unifying the Lagrange-based Apostol Hermite- Bernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We further dene Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we nd new and useful relations between the unied family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are obtained by using dierent analytical means and applying generating functions.