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Laplace's Equation--Bipolar Coordinates

In 2-D Bipolar Coordinates, Laplace's Equation is

\begin{displaymath}
{(\cosh v-\cos u)^2\over a^2}\left({{\partial F^2\over\partial u^2}+{\partial F^2\over\partial v^2}}\right)=0,
\end{displaymath} (1)

which simplifies to
\begin{displaymath}
{\partial F^2\over\partial u^2}+{\partial F^2\over\partial v^2}=0,
\end{displaymath} (2)

so Laplace's Equation is separable, although the Helmholtz Differential Equation is not.




© 1996-9 Eric W. Weisstein
1999-05-26