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) {colon equals} ∫¹₀ ∫¹₀ [x^αy^β log^lx log^jy]f{hook}(x, y)g(λx^ay^b) dx dy, where f{hook} 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.