Consider the harmonic function $u(x,y) = 1 - y + x/(x^2+y^2)$ on the upper half plane $y > 0$. What is the corresponding harmonic function on the first quadrant $x>0$, $y>0$, under the transformation $\mathbb Z \mapsto \mathbb Z^2$?
Have no idea how to do this. It is a homework problem and if I understand how to do just one I think I can do the rest myself, but this is a new section and the teachers really is not that good, but hey what math teacher is?