Asymmetric divergences at the Mach angle, for β = 1.1 . The solid and dashed curves trace and g_-2, respectively, close to the Mach angle θ_M, marked here by the vertical, dotted line. The functions diverge antisymmetrically once we choose C² = 1 . Both curves are taken from the numerical integration outlined in Sect. 4.5. The shaded region is that which we remove before enforcing continuity of f₀ and g_-2 across the cones.