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

Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry