Asymptotic evaluation of $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1193-1202
https://doi.org/10.4134/CKMS.c200133
Published online August 4, 2020
Printed October 31, 2020
Jan-Christoph Schlage-Puchta
Ulmenstra\ss e 69, Haus 3
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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