ON GENERALIZATION OF WEIERSTRASS APPROXIMATION THEOREM FOR A GENERAL CLASS OF POLYNOMIALS AND GENERATING FUNCTIONS

Abstract

Here, in this work we present a generalization of the Weierstrass Approximation Theorem for a general class of polynomials. Then we generalize it for two variablecontinuous function F (x, t) and prove that on a rectangle [a, b]× (-1, 1), a <= x <=b,|t|<1, a, b, t ? R , it uniformly converges into a generating function.As a result,we areable to apply our theorems to derive a number of generating functions.