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 variable continuous 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 are able to apply our theorems to derive a number of generating functions.