Bernstein polynomials and bernstein power series

PFollowing G.G.Lorentz\u27s book, Bernstein Polynomials, we develop in the first part of this paper the basic properties of the polynomials in the real and complex domains. These results along with certain properties of Legendre polynomials are used to establish Kantorovitch\u27s theorems on the convergence of Bernstein polynomials in special regions of the complex plane