We present simplified formulæ for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-to-use C++ library that allows computations in arbitrary precision arithmetic which is also documented here. We describe how these results can be combined with fast multipole methods to evaluate the Newton potential of more general, non-polynomial densities.

中文翻译：

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长方体上牛顿势的解析积分及其在快速多极方法中的应用

我们提出了简化的公式，用于在二维和三维空间中的盒子上多项式的牛顿势的解析积分。这些是在一个易于使用的 C++ 库中实现的，该库允许以任意精度算术进行计算，此处也记录了这一点。我们描述了如何将这些结果与快速多极方法相结合，以评估更一般的非多项式密度的牛顿势。