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Proceedings of the American Mathematical Society

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

 

 

Derivatives of polynomials with positive coefficients


Author: A. K. Varma
Journal: Proc. Amer. Math. Soc. 83 (1981), 107-112
MSC: Primary 26C05; Secondary 26D05, 41A17
MathSciNet review: 619993
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Abstract: Let $ {P_n}(x)$ be an algebraic polynomial of degree $ n$ with positive coefficients. We set

$\displaystyle {I_n} = \frac{{\vert\vert P'_n(x)\omega (x)\vert{\vert _{{L_2}[0,\infty )}}}}{{\vert\vert{P_n}(x)\omega (x)\vert{\vert _{{L_2}[0,\infty )}}}}.$

In this work upper bounds of $ I_{n}$ are investigated. We restrict ourselves here with the case $ \omega (x) = {x^{\alpha /2}}{e^{ - x/2}}$. Reslts are shown to be best possible.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0619993-0
Article copyright: © Copyright 1981 American Mathematical Society