Abstract
The Neumann problem for the unit n-dimensional sphere $S_n $, $n \geqq 2$, is the problem of finding a function $u(x_1 , \cdots ,x_n )$ which is harmonic inside $S_n $ provided we know the normal derivative of u on the boundary. Formulas are given to approximate u at a given specified point inside $S_n $. The construction of these formulas depends on knowing harmonic interpolation formulas for the surface of $S_{n - 1} $.
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