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arXiv · 1710.01270

A Gronwall-type Trigonometric Inequality

A. G. Smirnov
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Abstract

We prove that the absolute value of the $n$th derivative of $\cos(\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos(\sqrt{x})$.

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A. G. Smirnov. 2017-10-03. A Gronwall-type Trigonometric Inequality. https://doi.org/10.1080/00029890.2018.1436837

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