Prolate spheroidal harmonic expansion of gravitational field

Abstract

As a modification of the oblate spheroidal case, a recursive method is developed to compute the point value and a few low-order derivatives of the prolate spheroidal harmonics of the second kind, Qnm (y), namely the unnormalized associated Legendre function (ALF) of the second kind with its argument in the domain, 1 < y < ∞. They are required in evaluating the prolate spheroidal harmonic expansion of the gravitational field in addition to the point value and the low-order derivatives of , the 4π fully normalized ALF of the first kind with its argument in the domain, |t| ≤ 1. The new method will be useful in the gravitational field computation of elongated celestial objects. © 2014. The American Astronomical Society. All rights reserved..