Alternative derivations for the Poisson integral formula

Abstract

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson integral formula are also derived. Two and three-dimensional cases are considered. Also, interior and exterior problems are both solved. Even though the image concept is required, the location of image point can be determined straightforward through the degenerate kernels instead of the method of reciprocal radii.