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arXiv · 1704.08144

Inequalities and Asymptotics for some Moment Integrals

Faruk Abi-Khuzam
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Abstract

For $\alpha>\beta-1>0$, we obtain two sided inequalities for the moment integral $I(\alpha,\beta)= \int_{\mathbb{R}} |x|^{-\beta}|\sin x|^{\alpha}dx$. These are then used to give the exact asymptotic behavior of the integral as $\alpha \to \infty$. The case $I(\alpha,\alpha)$ corresponds to the asymptotics of Ball's inequality, and $I(\alpha,[\alpha]-1)$ corresponds to a kind of novel "oscillatory" behavior.

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Faruk Abi-Khuzam. 2017-04-26. Inequalities and Asymptotics for some Moment Integrals. https://arxiv.org/abs/1704.08144

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