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The theory of spherical and ellipsoidal harmonics
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The transformation of Laplace's equation in polar coordinates and the Legendres associated functions can be found in this article, where the authors also give approximate values of the generalized Legendres functions.Abstract:
Preface 1. The transformation of Laplaces's equation 2. The solution of Laplace's equation in polar coordinates 3. The Legendres associated functions 4. Spherical harmonics 5. Spherical harmonics of general type 6. Approximate values of the generalized Legendres functions 7. Representation of functions by series 8. The addition theorems for general Legendres functions 9. The zeros of Legendres functions and associated functions 10. Harmonics for spaces bounded by surfaces of revolution 11. Ellipsoidal harmonics List of authors quoted General index.read more
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