1990/02/21 by T. Miloh · 1 citation
Physics and Astronomy · Mathematics · Chemistry · #Scientific Research and Discoveries #Ellipsoid #Spheroid #Legendre polynomials #Prolate spheroid #Oblate spheroid #Homogeneous #Prolate spheroidal coordinates #Legendre function #Mathematical analysis #Mathematics #Spherical coordinate system #Associated Legendre polynomials #Physics #Geometry #Classical mechanics #Combinatorics #Chemistry #Orthogonal polynomials #Classical orthogonal polynomials #Gegenbauer polynomials
paper · pdf · doi:10.1088/0305-4470/23/4/027
openalex publication_date 1990/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Expressions for the interior and exterior potentials of a homogeneous ellipsoid are given in terms of ellipsoidal coordinates and Lame polynomials. It is shown that Wang's (1988,9) corresponding solutions for spheroidal bodies may be considered as special cases of these general triaxial expressions. Wang's results are also readily obtained by employing the relationship between the Lame and the Legendre polynomials in the case where the ellipsoid is degenerated into an oblate or prolate spheroid.