A note on the potential of a homogeneous ellipsoid in ellipsoidal coordinates

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.