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I need to find the Green's function for $$\Delta u=0$$ in the upper half plane subject to $$G(x,0;x_0,y_0)=0=\lim_{y\rightarrow\infty} G.$$ I know that $\Delta G=0$ and I have tried solving this with the free-space Greens and by setting it up and solving for $G$ with separation of variables. None of my work goes anywhere.

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