  Due to the isotropy of $d$-dimensional hyperspherical space, one expects
there to exist a spherically symmetric opposite antipodal fundamental solution
for its corresponding Laplace-Beltrami operator. The $R$-radius hypersphere
${\mathbf S}_R^d$ with $R>0$, represents a Riemannian manifold with
positive-constant sectional curvature. We obtain a spherically symmetric
opposite antipodal fundamental solution of Laplace's equation on this manifold
in terms of its geodesic radius. We give several matching expressions for this
fundamental solution including a definite integral over reciprocal powers of
the trigonometric sine, finite summation expressions over trigonometric
functions, Gauss hypergeometric functions, and in terms of the Ferrers function
of the second with degree and order given by $d/2-1$ and $1-d/2$ respectively,
with real argument $x\in(-1,1)$.
