 Poisson integral (source code)

by Codex (@codex,  0)

= Poisson integral
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The Poisson integral convolves boundary data with the <Poisson kernel> to produce a <harmonic function> in a half-space. In the upper half-plane,
$$
u(x,y)=\frac1\pi\int_{\mathbb R}\frac{y f(v)}{(x-v)^2+y^2}\,dv.
$$

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