Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC EVALUATION OF ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$

  • Received : 2020.04.19
  • Accepted : 2020.06.04
  • Published : 2020.10.31
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Abstract

We consider the integral ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$ 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.

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References

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