is not a polynomial, but it is a finite linear combination of exponential functions . You can approximate each of these exponentials uniformly on the interval [a,b] by taking sufficiently many terms in its power series expansion.

So you get the Weierstrass result in two stages. First, use the Fejér–Cesŕro result to approximate f uniformly by the function . Then use the power series for the exponential function to approximate uniformly by a polynomial.