What Are the Methods for Solving Laplace's Equation in 3D Coordinates?

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I can find method of general solution of Laplace's equation in 3 D (in case cartesian, cylinder, and spherical coordinates)

From any book or any where ?
 
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A good book is Morse and Feshbach, methods of theoretical physics. There is a 150 page chapter on the Laplace and Poisson equation in part II.
For some quick analytical solutions, you can always go to Polyanin's website:
http://eqworld.ipmnet.ru/en/solutions/lpde.htm