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An extremal problem for polynomials with a prescribed zero. II


Authors: Q. I. Rahman and G. Schmeisser
Journal: Proc. Amer. Math. Soc. 73 (1979), 375-378
MSC: Primary 30A10; Secondary 26D05
DOI: https://doi.org/10.1090/S0002-9939-1979-0518524-4
MathSciNet review: 518524
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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 _{\vert z\vert = 1}}\vert{p_n}(z)\vert \leqslant 1$, then $ \vert{p_n}(0)\vert < 1 - (1.03369)/n + O(1/{n^2})$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0518524-4
Keywords: Extremal problem, polynomials with a prescribed zero
Article copyright: © Copyright 1979 American Mathematical Society

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