It seems that popular textbooks on electrodynamics do not discuss how to solve the Laplace equation in ellipsoidal coordinates. I could not find any reference, but there must be references about this. Could anyone give a reference?
As an example, the question can be how to calculate the charge distribution on an ellipsoid by solving the Laplace equation. (I know there is a way to solve this particular problem without solving the Laplace equation, but I want to know how the ellipsoidal coordinates works.)