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Ellipsoidal Harmonics by George Dassios

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9The elliptic functions approach

In the present chapter we provide a limited introduction to the definitions of the classical elliptic functions and their connection to the theory of Lamé functions and ellipsoidal harmonics. This will facilitate the translation of any results, given in the literature in terms of elliptic functions, to the corresponding results in terms of Lamé functions, and vice versa. There are two different ways to introduce the theory of ellipsoidal harmonics in terms of elliptic functions. The first approach is based on the Weierstrass elliptic function images, and the second one is based on the Jacobi elliptic functions sn, cn, ...

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