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What is a general solution of biharmonic equation $\nabla^2\nabla^2f=0$ in spherical coordinates?

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.

According to Oberbeck, A., Crelle, 62, 1876, a general solution of biharmonic equation in spherical coordinates is $\label{eq:Fsol} F=\sum_{n=0}^{\infty}\frac{A_n+B_nr^2}{r^{2n+1}}r^nK_n \;, $ where $K_n$ is a spherical function of order $n$. How to show that this holds (if it does)?

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