The best uniform polynomial approximation to class of the form 1(a2±x2)

Using Chebyshev expansion properties we obtain explicitly the best uniform polynomial approximation out of P2nP2n to a class of rational functions of the form 1/(a2±x2)1/(a2±x2) on [−c,c][−c,c]. In this way we give some new theorems about the best approximation of this class of rational functions. Furthermore we obtain the alternating set of this class of functions.