# Method of Images again

#### OliviaB

Apply the method of images to derive the solution

$$\displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0$$

from

$$\displaystyle \bigtriangledown^2 \phi (x,y,z) = 0$$

$$\phi(x,y,0) = f(x,y)$$

from the region $$- \infty < x < \infty, - \infty < y < \infty, 0 < z < \infty$$

Its hard for me to start because I dont really understand the method of images.

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