论文标题
拉普拉斯方程基本解决方程的膨胀环境坐标的扩展
Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates
论文作者
论文摘要
我们得出了在三维欧几里得空间中扁平环坐标中拉普拉斯方程基本解的扩展。这种扩展是在“扁平环”的内部和外部谐波的功能的双重系列。这些内部和外部扁平谐波函数以简单的周期性拉梅功能表示。在限制情况下，我们获得了在环形坐标中基本溶液的扩展。
We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of "flat rings". These internal and external flat-ring harmonic functions are expressed in terms of simply-periodic Lamé functions. In a limiting case we obtain the expansion of the fundamental solution in toroidal coordinates.
