  We derive all eighteen Gauss hypergeometric representations for the Ferrers
function of the second kind, each with a different argument. They are obtained
from the eighteen hypergeometric representations of the associated Legendre
function of the second kind by using a limit representation. For the 18
hypergeometric arguments which correspond to these representations, we give
geometrical descriptions of the corresponding convergence regions in the
complex plane. In addition, we consider a corresponding single sum Fourier
expansion for the Ferrers function of the second kind. In four of the eighteen
cases, the determination of the Ferrers function of the second kind requires
the evaluation of the hypergeometric function separately above and below the
branch cut at $[1,\infty)$. In order to complete these derivations, we use
well-known results to derive expressions for the hypergeometric function above
and below its branch cut. Finally we give a detailed review of the 1888 paper
by Richard Olbricht who was the first to study hypergeometric representations
of Legendre functions.
