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 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.c200133Published online August 4, 2020Printed 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 Downloads: Full-text PDF   Full-text HTML