Left: β (the leading nonzero power-law index of the pressure) as a function of n for γ = 5/3 (blue) and γ = 4/3 (orange) and m = 3. Since β > 0, the pressure converges near the CD, but the rate of convergence is extremely slow as n → 3. Right: the self-similar pressure in the RS shell, h _r, as a function of −η on a logarithmic scale. The numerical accuracy needs to be extremely high, with the functions resolved at ∣η∣ ≤ 10⁻¹¹ for n = 2 and ∣η∣ ≤ 10⁻¹⁶ for n = 2.5, to correctly determine the pressure at the CD and thus the eigenvalues controlling the expansion of the RS shell and the deceleration of the CD.