- #1

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"[...]

[tex]

\left[\frac{\partial}{\partial R^2}+\frac{sin \phi}{R^2}\frac{\partial}{\partial\phi}\left(\frac{1}{sin\phi}\frac{\partial}{\partial\phi}\right)\right]^2 \psi = 0

[/tex]

This is satisfied by

[tex]

\psi = sin^2 \phi f(R)

[/tex]

if

[tex]

\left(\frac{d^2}{dR^2}-\frac{2}{R^2}\right)^2 f(R) = 0

[/tex]

The solution of the prior equation is

[tex]

f(R) = \frac{A}{R} + BR + CR^2 + DR^4

[/tex]

[...]"