Green’s theorem and Green’s identities are well-known and their uses span almost every branch of science and mathematics. In this paper, we derive a vector analogue of Green’s three scalar identities and consider some of their uses. We also offer a number of historical tidbits in connection to the work of George Green.

中文翻译：

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向量化格林的身份

格林定理和格林恒等式是众所周知的，它们的用途几乎涵盖科学和数学的每个分支。在本文中，我们推导出格林的三个标量恒等式的向量模拟并考虑它们的一些用途。我们还提供了一些与乔治格林的工作有关的历史花絮。