PROLATE SPHEROIDAL HARMONIC EXPANSION OF GRAVITATIONAL FIELD

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, Q(nm) (y), namely the unnormalized associated Legendre function (ALF) of the second kind with its argument in the domain, 1 < y < infinity. 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 (P) over bar (nm) (t), the 4 pi fully normalized ALF of the first kind with its argument in the domain, vertical bar t vertical bar <= 1. The new method will be useful in the gravitational field computation of elongated celestial objects.