Derivatives of polynomials with positive coefficients

Varma, A. K.

doi:10.1090/S0002-9939-1981-0619993-0

Derivatives of polynomials with positive coefficients
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by A. K. Varma

Proc. Amer. Math. Soc. 83 (1981), 107-112

DOI: https://doi.org/10.1090/S0002-9939-1981-0619993-0

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Abstract:

Let ${P_n}(x)$ be an algebraic polynomial of degree $n$ with positive coefficients. We set \[ {I_n} = \frac {{||P’_n(x)\omega (x)|{|_{{L_2}[0,\infty )}}}}{{||{P_n}(x)\omega (x)|{|_{{L_2}[0,\infty )}}}}.\] 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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