An extremal problem for polynomials with a prescribed zero. II

Rahman, Q. I.; Schmeisser, G.

doi:10.1090/S0002-9939-1979-0518524-4

An extremal problem for polynomials with a prescribed zero. II
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by Q. I. Rahman and G. Schmeisser

Proc. Amer. Math. Soc. 73 (1979), 375-378

DOI: https://doi.org/10.1090/S0002-9939-1979-0518524-4

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Abstract:

Improving upon an earlier estimate it is shown that if ${p_n}(z)$ is a polynomial of degree at most n such that ${p_n}(1) = 0$ and ${\max _{|z| = 1}}|{p_n}(z)| \leqslant 1$, then $|{p_n}(0)| < 1 - (1.03369)/n + O(1/{n^2})$.

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