Consider an integral with a point singularity in its integrand, such as ρ^−α or \(\log \rho \). We introduceand discuss two methods for approximating such integrals, in both two and three dimensions. The methods are first introduced using the unit disk as the quadrature region, and then, they are extended to other regions and to three dimensions. The error behavior of the numerical integration for singular points near to the boundary is examined.

中文翻译：

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奇异积分的多元正交

考虑一个在积分中具有点奇点的积分，例如ρ ^{− α}或\（\ log \ rho \）。我们在二维和三维中介绍并讨论了两种逼近此类积分的方法。首先使用单位圆盘作为正交区域介绍这些方法，然后将其扩展到其他区域和三个维度。检查了靠近边界的奇异点的数值积分的误差行为。