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Ellipsoidal Harmonics by George Dassios

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3Lamé functions

3.1 The Lamé classes

In the spherical system (r, v, φ), with

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the interior spherical harmonic functions are given by

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where Pnm are the well-known associated Legendre functions [183]. First, we show how we can express these harmonic functions in terms of harmonic polynomials, i.e. polynomials in (x1, x2, x3) which satisfy Laplace’s equation. From the definition of the associated Legendre functions (see Appendix C) we have

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Furthermore, ...

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