Inequalities and asymptotics for some moment integrals
Abstract For α > β − 1 > 0 $\alpha>\beta-1>0$ , we obtain two-sided inequalities for the moment integral I ( α , β ) = ∫ R | x | − β | sin x | α d x $I(\alpha,\beta)=\int_{\mathbb{R}}|x|^{-\beta}|\sin x|^{\alpha}\,dx$ . These are then used to give the exact asymptotic behavior of the int...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1532-7 |