Analytical Computation of Hyper-Ellipsoidal Harmonics
George Dassios,
George Fragoyiannis
Abstract:The four-dimensional ellipsoid of an anisotropic hyper-structure corresponds to the four-dimensional sphere of an isotropic hyper-structure. In three dimensions, both theories for spherical and ellipsoidal harmonics have been developed by Laplace and Lamé, respectively. Nevertheless, in four dimensions, only the theory of hyper-spherical harmonics is hitherto known. This void in the literature is expected to be filled up by the present work. In fact, it is well known that the spectral decomposition of the Lapl… Show more
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