Asymptotic Expansion of a Multiple Integral

Abstract:

An alternative derivation is given for the asymptotic expansion, as s → 0⁺, of the multiple integral

where g ∈ 𝔂(ℝ) and f ∈ C^∞(ℝⁿ). 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.