Polynomial approximation errors for functions of low-order continuity

Given a function f defined on [-1, 1] we obtain, in terms of (n+1)st divided differences, expressions for the minimax error E n(f) and the error S n(f) obtained by truncating the Chebyshev series off after n+1 terms. The advantage of using divided differences is that f is required to have no more than a continuous second derivative on [-1, 1].