The best uniform polynomial approximation to class of the form 1 a4-x4

Abstract EN

It is very useful to be able to replace any given function by a simpler function, such as a polynomial, chosen to have values not identical with but very close to those of the given function.

and as it is known best approximation by polynomials is an important subject in approximation theory and has a large number of applications such as the numerical computation of a best approximating polynomial , partial differential equations , differential equations etc…..

in this paper we determine the best uniform polynomial approximation out of (the space of polynomials of degree at most) to a class of rational functions of the form 1 / a4-x4 on , [-c, c].

in this way we introduce a theorem about the best approximation of this class of rational function and we also obtain Chebyshev alternative set of these classes of functions.