Mapping-out function of a vertical slit ($g(z)=x+\sqrt{(z-x{)}^2+h^2}$)

For the compact H-hull $(x,x+ih]$, the square-root branch asymptotic to $z-x$ gives the hydrodynamic normalization at infinity of its mapping-out function of a compact H-hull. Its expansion has coefficient $h^2/2$, the half-plane capacity of a vertical slit.