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Integral representation formulas are derived for the solution of the polyharmonic equation in an n-dimensional hypersphere and in an n-dimensional half-space when the normal derivatives
are given on the boundaries of these domains. The solution method utilizes the Goursat-Almansi formula to represent an m-polyharmonic function in terms of m harmonic functions for the given domain. The harmonic functions are then determined from an iteratively denned system of m Dirichlet problems.
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