A new class of 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 using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli polynomials studied by Pierpaolo Natalini and Angela Bernardini, Bernoulli numbers, Bernoulli polynomials and Hermite polynomials.