SUMMARY
In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials F_{n}^{(a)}(x,?) of degree n and order a introduced by Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials B_n(x), generalized Bernoulli numbers B_n(a,b), generalized Bernoulli polynomials B_n(x;a,b,c) of Luo et al, Hermite-Bernoulli polynomials {_HB}_n(x,y) of Dattoli et al and {_HB}_n^{(a)} (x,y) of Pathan are generalized to the one {_HB}_n^{(a)}(x,y,a,b,c) which is called the generalized polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x), B_n(a,b), B_n(x;a,b,c) and {}_HB_n^{(a)}(x,y;a,b,c) are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials