Asymptotic evaluation of $\int_0^\infty(\sin x/x)^ndx$
Commun. Korean Math. Soc.
Published online August 4, 2020
Jan-Christoph Schlage-Puchta
University of Rostock
Abstract : We consider the integral $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$ as a function of the positive integer $n$. We show that there exists an asymptotic series in $\frac{1}{n}$ and compute the first terms of this series together with an explicit error bound.
Keywords : sine integral, asymptotic expansion
MSC numbers : 26D15, 33F05
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