A New Class of Generalized Polynomials Associated with Hermite and Euler Polynomials

In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials of degree n and order alpha introduced by Dere and Simsek. The concepts of Euler numbers E (n) , Euler polynomials E (n) (x), generalized Euler numbers E (n) (a, b), generalized Euler polynomials E (n) (x; a, b, c) of Luo et al., Hermite-Bernoulli polynomials of Dattoli et al. and of Pathan are generalized to the one which is called the generalized polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between E (n) , E (n) (x), E (n) (a, b), E (n) (x; a, b, c) and are established. Some implicit summation formulae and general symmetry identities are derived using different analytical means and applying generating functions.