SPECIAL STRUCTURED REPRESENTATIONS FOR BERNSTEIN POLYNOMIALS OF RATIONAL MODULE FUCTION
Classical Bernstein polynomials of rational module function on a standard interval are studied. On particular example, typical effects are analyzed in detail. Analogues of Popoviciu expansion with a new representation of Bernstein polynomials in the form of special structured sums are given. The question of the exact convergence domain of expansion is discussed. It is pointed out the boundary of the convergence domain associates with the distribution of zeros of the Bernstein polynomials.