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Ellipsoidal Harmonics by George Dassios

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Appendix GMiscellaneous relations

In solving boundary value problems, and in particular in reducing expressions from ellipsoidal to spheroidal and spherical geometry, one has to prove certain identities that eliminate the existing indeterminancies of the ellipsoidal system. In most cases, this problem is focussed in finding the appropriate combination of terms that allow the mutual cancellation of singularities, as the ellipsoidal system degenerates to systems with higher symmetry. Once these relations are found, they are proved by long and tedious calculations. Since these relations appear frequently in applied problems we list some of them here and we leave their proofs as exercises.

G.1 Relations among constants

The semi-axes of the reference ...

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