Poisson kernel for the upper half-plane
= Poisson kernel for the upper half-plane
{c}
{title2=$P_y(x)=\dfrac1\pi\dfrac{y}{x^2+y^2}$}
For the <complex upper half-plane>, the Poisson kernel is
$$
P_y(x-v)=\frac1\pi\frac{y}{(x-v)^2+y^2}.
$$
It is the density of <harmonic measure> on the real boundary as viewed from $x+iy$.
= Poisson kernel
{synonym}