Error Bernoulli Polynomials and their Relations to Hermite Polynomials

Abstract

In this thesis, we discuss about a family of polynomials Bn( 1 2 , x) called Error Bernoulli Polynomials. These polynomials were first considered by Abdul Hassen and H.D.Nguyen as residues that emerge from error zeta function. Later, H.L.Geletah consedered these poly nomials interms of their relation to the Hermite polynomials. In this thesis we consider further properties of Bn( 1 2 , x) and discuss more relation to Hermite polynomials.