A Gronwall-type Trigonometric Inequality

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 $n=0,1,\dots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos (\sqrt{x})$.

4 pages, a misprint corrected

Cited by in corpus (1)

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