Barenblatt's textbooks on scaling use the following example: $\zeta = F(z)$ is an analytic function that carries out a conformal mapping of the exterior of the triangle (the cross section of the wedge in the flow) onto the exterior of the segment $0 \leq x \leq a$ of the x-axis such that $d\zeta/dz \to 1$ as $z \to \infty$. The altitude of the triangle is $L$ and angle at its apex $2 \alpha$. From Schwartz-Christoffel,
$z = \int\limits_0^\zeta t^{-\alpha/\pi} (t-a)^{-1/2} (t-b)^{1/2+\alpha/\pi} dt$
where $a = F(L)$ and $b = F(L + iL\tan{\alpha})$
This is not the usual form of Schwartz-Christoffel, since it involves mapping the exterior of the polygon. Where does this formula come from? How are the interior angles defined? They don't seem to correspond to $\alpha$, $\pi/2$, and $\pi/2 - \alpha$, as I might expect from half of the given triangle. Any clues?