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It is known the Poisson's integral formula : Let $f(z)$ be analytic inside and on the circle $\mathcal{C} : \vert z \vert = R$, and let $z =re^{i \theta}$ be any point inside $\mathcal{C}$ so :

$$ f(re^{i \theta}) = \dfrac{1}{2\pi} \int_{0}^{2\pi} \dfrac{R^2-r^2}{R^2 - 2Rr\cos(\theta - \phi) + r^2}f(Re^{i \phi})\,d\phi $$

In one task they ask me to find the Poisson's integral formula (if possible) in a square.

How could I do it?. I was thinking of doing the same for the case of the circle but I don't know if that's what the problem refers to. Any help or hint it would help me a lot.

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