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Let in, denote the class of polynomials p,(X) =n = akXk of degree n which satisfy pn(x)l <(1 -x2)112 for -1 <x< 1. Given any xo in [-1, 1], how large can np (x0)l (the kth derivative at xo) be if pn(x) belongs to the class 7 In case xo=O the problem is equivalent to the problem of estimating lakl ifpn(X) = :kn= O akXk E Cn. It has been shown [3] that if pn(x) = o axk EeTn then lail < n-1, Ia21 < {(n-1)2+1}/2. Here we prove the following theorem which gives a sharp estimate for each of the coefficients.

Addendum to: “On a problem of Turán about polynomials with curved majorants”