Some Implicit Summation Formulas and Symmetric Identities for the Generalized Hermite–Bernoulli Polynomials

In this paper, we introduce a new class of generalized Hermite–Bernoulli polynomials and derive some implicit summation formulae and symmetric identities by applying the generating functions. These results extend some known summations and identities of generalized Hermite–Bernoulli polynomials studied by Dattoli et al., Natalini et al., Zhang et al., Yang and Pathan.