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.