Commun. Korean Math. Soc. 2020; 35(4): 1193-1202
Online first article August 4, 2020 Printed October 31, 2020
https://doi.org/10.4134/CKMS.c200133
Copyright © The Korean Mathematical Society.
Jan-Christoph Schlage-Puchta
Ulmenstra\ss e 69, Haus 3
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
2003; 18(4): 755-765
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