Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 1 / 36E / iii / Solution

For $3\pi /2<2\alpha <2\pi$, $1/2<{\lambda }_0<2/3$ and $3/2<{\lambda }_1<2$, whereas ${\lambda }_2>5/2$. Hence both of the first two harmonic modes precede the $r^2$ particular term in the corner expansion; the first still dominates as $r\to 0$. The first-mode gradient is singular. These are reentrant wedges, and the global arc condition determines the important homogeneous coefficients.