On the three families of extended Laguerre-based Apostol-type polynomials

In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite Bell-Hermite find representations. We derive some implicit summation formulae symmetric identities for these families special functions by applying the generating functions.