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

ON GENERALIZATION OF WEIERSTRASS APPROXIMATION

THEOREM FOR A GENERAL CLASS OF POLYNOMIALS AND

GENERATING FUNCTIONS

*HEMANT KUMAR, M. A. PATHAN*

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## Abstract

Here, in this work we present a generalization of theWeierstrass 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; jtj<1; a; b; t 2 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.

## Keywords

Weierstrass Approximation Theorem, Bernstein Approximation theorem,

generalization of Weierstrass Approximation Theorem, generating functions.