scholarly journals Fundamental Solution of Laplace's Equation in Hyperspherical Geometry

2011 ◽  
Author(s):  
Howard S. Cohl
Keyword(s):  
Fundamental Solution ◽  
Laplace’S Equation ◽  
Laplace's Equation

Expansions for a fundamental solution of Laplace's equation on ℝ3 in 5-cyclidic harmonics

2014 ◽  
Vol 12 (06) ◽  
pp. 613-633
Author(s):  
Howard S. Cohl ◽  
Hans Volkmer
Keyword(s):  
Differential Equation ◽  
Euclidean Space ◽  
Fundamental Solution ◽  
Three Dimensional ◽  
Singular Points ◽  
Dimensional Euclidean Space ◽  
Laplace’S Equation ◽  
Eigenfunction Expansions ◽  
Laplace's Equation

We derive eigenfunction expansions for a fundamental solution of Laplace's equation in three-dimensional Euclidean space in 5-cyclidic coordinates. There are three such expansions in terms of internal and external 5-cyclidic harmonics of first, second and third kind. The internal and external 5-cyclidic harmonics are expressed by solutions of a Fuchsian differential equation with five regular singular points.

scholarly journals Note on the electric capacity coefficients of spheres

1912 ◽  
Vol 87 (598) ◽  
pp. 485-487
Keyword(s):  
General Solution ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Electric Capacity ◽  
Physical Problems

In the 'Proceedings' of the Society, vol. 87, p. 109, Mr. Jeffery obtains a general solution of Laplace’s equation in a form suitable for physical problems in connection with two spheres. As an illustration he applies his solution to the problem of finding the capacity coefficients of two equal spheres, obtaining a result which he shows to be equivalent to one of Maxwell’s series formulæ. He then computes a table of the numerical values of these coefficients.

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