A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
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DOI：
10.3842/sigma.2016.079
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发表时间：
2016-01-01
影响因子：
0.9
通讯作者：
Chapling, Richard
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文献类型：
--
作者：
Chapling, Richard
考虑非齐次项积分为零的n维球上的泊松方程。利用一些经典的和现代的超几何恒等式，我们对这个方程进行积分，得到任意维的广义超几何函数的基本解的形式，在奇、偶维情况下具有不同的封闭形式。
We consider Poisson's equation on the n-dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric identities, we integrate this equation to produce the form of the fundamental solutions for any number of dimensions in terms of generalised hypergeometric functions, with different closed forms for even and odd-dimensional cases.