An Alternative Method for the Asymptotic Expansion of a Double Integral

Abstract An alternative method is proposed in order to obtain, as λ → + ∞ , the asymptotic expansion of the double integral K(λ) ≔ ∫ 1 0 ∫ 1 0 [x α y β log l x log j y]ƒ(x, y)g(λx a y b ) dx dy, where ƒ is smooth enough and g belongs to A ( R ), a space defined in the text. This expansion is derived by employing a powerful tool - the integration in the finite-part sense of Hadamard.