On the asymptotic properties of a canonical diffraction integral

We introduce and study a new canonical integral, denoted $$ , depending on two complex parameters α ₁ and α ₂. It arises from the problem of wave diffraction by a quarter-plane and is heuristically constructed to capture the complex field near the tip and edges. We establish some region of analyticity of this integral in $$ , and derive its rich asymptotic behaviour as |α ₁ | and |α ₂ | tend to infinity. We also study the decay properties of the function obtained from applying a specific double Cauchy integral operator to this integral. These results allow us to show that this integral shares all of the asymptotic properties expected from the key unknown function G _+- arising when the quarter-plane diffraction problem is studied via a two-complex-variables Wiener-Hopf technique (see Assier & Abrahams, SIAM J. Appl. Math., in press). As a result, the integral $$ can be used to mimic the unknown function G _+- and to build an efficient 'educated' approximation to the quarter-plane problem.