English

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

Classical Analysis and ODEs 2021-03-09 v1

Abstract

We consider the integral 0(sinxx)n  dx\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx as a function of the positive integer nn. We show that there exists an asymptotic series in 1n\frac{1}{n} and compute the first terms of this series together with an explicit error bound.

Keywords

Cite

@article{arxiv.2010.11759,
  title  = {Asymptotic evaluation of $\int_0^\infty\left(\frac{\sin x}{x}\right)^n\;dx$},
  author = {Jan-Christoph Schlage-Puchta},
  journal= {arXiv preprint arXiv:2010.11759},
  year   = {2021}
}