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.