Given a polynomial of n+1th. order f(x)on -1 < x < 1, I want to find the polynomial of nth. order pn(x) that minimizes the maximum error. This is just minimax approximation, except that f(x) is a one degree higher polynomial. If f(x) = x^(n+1), then pn(x) = x^(n+1) -T_n+1(x)/2^n, where Tn(x) are the Chebyshev polynomials. My question is : If f(x) is a general polynomial of degree n+1, what is pn(x)?