On the asymptotic properties of a canonical diffraction integral.

We introduce and study a new canonical integral, denoted , depending on two complex parameters and . 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 | | and | | 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 arising when the quarter-plane diffraction problem is studied via a two-complex-variables Wiener-Hopf technique (see Assier & Abrahams, , in press). As a result, the integral can be used to mimic the unknown function and to build an efficient 'educated' approximation to the quarter-plane problem.