We introduce and study a new canonical integral, denoted I+−ε, depending on two complex parameters α1 and α2. 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 C2, and derive its rich asymptotic behaviour as |α1 | and |α2 | 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.

中文翻译：

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关于正则衍射积分的渐近性质

我们引入并研究了一个新的典型积分，表示为 I+−ε，取决于两个复数参数 α1 和 α2。它源于四分之一平面的波衍射问题，并启发式构造以捕获尖端和边缘附近的复杂场。我们在 C2 中建立该积分的某个解析域，并推导出其丰富的渐近行为为 |α1 | 和 |α2 | 趋于无穷。我们还研究了通过将特定的双柯西积分算子应用于该积分而获得的函数的衰减特性。这些结果使我们能够表明，当通过双复变量 Wiener-Hopf 技术研究四分之一平面衍射问题时，该积分具有关键未知函数 G+− 所预期的所有渐近特性（参见 Assier & Abrahams， SIAM J. Appl. Math.，印刷中）。其结果，