Inequalities and Asymptotics for some Moment Integrals

Faruk Abi-Khuzam

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…