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ksi
Jul23-08, 12:35 PM
It seems to be a well-known problem, but i cannot find any literature where it is solved. Any advise will be appreciated.

After the separation of variables i got the following equation of Sturm-Liouville type:

[(1-\eta^2)y']'- \frac{m^2(\xi^2+\eta^2)}{(1+\xi^2)(1-\eta^2)} y=\lambda(\eta^2+\xi^2)y

where \xi={\rm const}\geqslant 0, -1\leqslant\eta\leqslant 1 and \lambda is eigenvalue.