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Laplace's Equation--Bipolar Coordinates

In two-dimensional bipolar coordinates, Laplace's equation is

((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0,

which simplifies to

(partialF^2)/(partialu^2)+(partialF^2)/(partialv^2)=0,

so Laplace's equation is separable, although the Helmholtz differential equation is not.

See also

Bipolar Coordinates, Laplace's Equation

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Cite this as:

Weisstein, Eric W. "Laplace's Equation--Bipolar Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LaplacesEquationBipolarCoordinates.html

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