A new class of generalized polynomials associated with Hermite-Bernoulli polynomials

Abstract

In this thesis, we analysis the concept of a new class of generalized polynomials associated with Hermite-Bernoulli polynomials of ordera. This generalization is a unification formula of the Hermite polynomials,Bernoulli numbers, Generalized Bernoulli polynomials and generalized Hermite –Bernoulli polynomials HB( nf;a)(x;y;c) for two variable of order a and on real numbers c > 0 and other families of polynomials depending on any generating function f . Some implicit summation formulae and general symmetry identities are derived by using different analysis means and applying generating function. The result analysis here are a generalization of some known summation formulae earlier studied by Pathan and Kha