Asymptotic Expansion of a Multiple Integral

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • J. P. Mcclure
  • Sue Cheun Roderick WONG

Detail(s)

Original languageEnglish
Pages (from-to)1630-1637
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume18
Issue number6
Publication statusPublished - Nov 1987
Externally publishedYes

Abstract

An alternative derivation is given for the asymptotic expansion, as $s \to 0^ + $, of the multiple integral \[ J(s) = \int_{[0,1]^n } {g({{x^\alpha } / s})} x^\beta f(x)dx,\] where $g \in \mathcal {S}(\mathbb{R})$ and $f \in C^\infty (\mathbb{R}^n )$. The integral $J(s)$ is first expressed as a contour integral, in which the integrand is a meromorphic function in the complex plane. The asymptotic expansion is then obtained by moving the contour to the left, the terms of the expansion being the residues of the integrand.

Research Area(s)

  • asymptotic expansion, multiple integral, Mellin transform

Citation Format(s)

Asymptotic Expansion of a Multiple Integral. / Mcclure, J. P.; WONG, Sue Cheun Roderick.
In: SIAM Journal on Mathematical Analysis, Vol. 18, No. 6, 11.1987, p. 1630-1637.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review