Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

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.

Asymptotic evaluation of $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$

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