Unified Apostol Type Hermite-Bernoulli, Hermite-Euler and Hermite-Genocchi Polynomials

Abstract

In this paper, we introduce a new class of generalized Apostol type Hermite-Bernoulli, Apostol type Hermite-Euler and Apostol type Hermite-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite and Bell-Hermite polynomials and to find new representations. We derive some implicit summation formulae and symmetric identities for these introduced polynomials by using their generating functions. These results extend some known summation formulas and identities of generalized Hermite-Bernoulli polynomials studied by Dattoli et al., Natalini et al., Zhang et al., Yang, Pathan and Pathan and Khan.