  Prolate spin-weighted spheroidal harmonics play a key role in black-hole
perturbation theory. In particular, the highly damped quasinormal resonances of
rotating Kerr black holes are closely related to the asymptotic eigenvalues of
these important functions. We here present a novel and compact derivation of
the asymptotic eigenvalues of the prolate spin-weighted spheroidal harmonics.
Our analysis is based on a simple trick which transforms the corresponding
spin-weighted spheroidal angular equation into a Schr\"odinger-like wave
equation which is amenable to a standard WKB analysis. Our analytical results
for the prolate asymptotic spectrum agree with previous numerical computations
of the eigenvalues which appear in the literature.
