A method to obtain the best uniform polynomial approximation for the family of rational function

Abstract

In this article, by using Chebyshev's polynomials and Chebyshev's expansion, we obtain the best uniform polynomial approximation out of P_2n to a class of rational functions of the form (ax²+c)^-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax²+bx+c)^-1 for both cases b²-4ac L 0 and b²-4ac G 0. <br />