Bernstein's asymptotic best bound for the kth derivative of a polynomial (Q1066379)

A complete proof, which yields an error term showing a dependence on n and x, is given for Bernstein's result that the best bound on the kth derivative on polynomials of degree less than or equal to n, at a point x in (-1,1), is asymptotic to \((n/\sqrt{1-x^ 2})^ k\) as n tends to infinity.