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# Green's function and Poisson's integral formula

Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts):

I need to construct Green's function for the Dirichlet problem (Laplace's equation) in the upper half plane R={(x,y) : y>0} and I must derive Poisson's integral formula for the half plane.

Please note that I am unable to use mathematical symbols (my computer does not allow me.) I will thus write out the following hints. For the first part of the problem we may consider log(R*/R) where R=|x-y|, R*=|x*-y|, with x* the mirror image of x=(x,y) with respect to y=0.

I have also know that the Poisson equation may be:

u(x,y) = [y divided by pi] times the integral (from negative infinity to positive infinity) of [u(m,o) divided by (m-x)squared + ysquared]dm.

I just need help deriving all of this. I have some idea but I cannot show you what I have (too complicated.) Thank you so much for taking the time in trying this question.

#### Solution Summary

This shows how to construct Green's function for a given Dirichlet problem and derive Poisson's integral formula for the half plane.

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