Laplace's Equation--Bipolar Coordinates

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

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

which simplifies to

$${\partial F^2\over\partial u^2}+{\partial F^2\over\partial v^2}=0,$$ (2)

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