Physics – Mathematical Physics
Scientific paper
2011-08-18
SIGMA 7 (2011), 108, 14 pages
Physics
Mathematical Physics
misprints are corrected
Scientific paper
10.3842/SIGMA.2011.108
Due to the isotropy of $d$-dimensional hyperspherical space, one expects there to exist a spherically symmetric 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 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 associated Legendre function of the second kind on the cut (Ferrers function of the second kind) with degree and order given by $d/2-1$ and $1-d/2$ respectively, with real argument between plus and minus one.
No associations
LandOfFree
Fundamental Solution of Laplace's Equation in Hyperspherical Geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fundamental Solution of Laplace's Equation in Hyperspherical Geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fundamental Solution of Laplace's Equation in Hyperspherical Geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-180855