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In this paper, the harmonic functions of Laplace's equations are derived explicitly for the Dirichlet and the Neumann boundary conditions on the boundary of a sector. Those harmonic functions are more explicit than those of Volkov [Volkov EA, Block method for solving the Laplace equation and for constructing conformal mappings. Boca Raton: CRC Press; 1994], and easier to expose the mild singularity...
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