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 < ∞. 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 nm

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... ), 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.