An Alternative Method for the Asymptotic Expansion of a Double Integral

An alternative method is proposed in order to obtain, as λ → + ∞ , the asymptotic expansion of the double integral K(λ) ≔ ∫10 ∫10 [xαyβ loglx logjy]ƒ(x, y)g(λxayb) 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.