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What is the solution of the biharmonic equation \begin{equation} \nabla^2\nabla^2 f=0 \end{equation} in oblate spheroidal coordinates?

The general solution of Laplace's equation $\nabla^2 f=0$ in oblate spheroidal coordinates is known as an oblate spheroidal harmonic. According to Wikipedia any solution of Laplace equation is also a solution of biharmonic equation, but the vice versa is not always true. Therefore I assume there exists a more general solution of the biharmonic equation.

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    @doraemonpaul: Please stop flooding the frontpage with many edits on the same day. If you continue, limit yourself to only a few per day please.2012-09-03

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