We introduce and study a new canonical integral, denoted
I
+
−
ε
, 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
C
2
, 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
I
+
−
ε
can be used to mimic the unknown function
G
+−
and to build an efficient ‘educated’ approximation to the quarter-plane problem.
A Surprising Observation in the Quarter-Plane Diffraction Problem
