Let $R >0$, and let $h(Re^{i \theta})$ be a continuous function on the circle $\{ |z|=R \}$. Show that the function
$\tilde{h}(z)=\int^{\pi}_{-\pi} \frac{R^2-r^2}{R^2+r^2-2rR\cos(\theta - \phi)}h(Re^{i \phi}) \frac{d \phi}{2 \pi}, |z|,
is harmonic on the disk $\{ |z| and has boundary values $h(Re^{i \theta})$ on the boundary circle.