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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a problem of Turan about polynomials


Authors: R. Pierre and Q. I. Rahman
Journal: Proc. Amer. Math. Soc. 56 (1976), 231-238
MSC: Primary 26A75
DOI: https://doi.org/10.1090/S0002-9939-1976-0412362-6
MathSciNet review: 0412362
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Abstract: It is shown that if $ {p_n}(x)$ is a polynomial of degree $ n$ whose graph on the interval $ - 1 < x < 1$ is contained in the unit disk then the absolute value of its second derivative cannot exceed $ \tfrac{2}{3}(n - 1)(2{n^2} - 4n + 3)$ on $ [ - 1,1]$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0412362-6
Keywords: Polynomials with curved majorants, Tchebycheff polynomial of the first kind, Tchebycheff polynomial of the second kind
Article copyright: © Copyright 1976 American Mathematical Society