Incomplete beta function I_ξ(a,b) (black contours) for a = (n − 1)/2 and b = 1/2 as function of ξ = 1 − y_n. The lines are labeled with the corresponding power n. The line for a power n = 3 is emphasized through a thick line. The gray lines correspond to ξ = q^{2 /n} for fixed density ratio q and varying power n. The lines are labeled with log ₁₀q. The gray dashed lines are obtained using the approximation of the incomplete beta function (Eq. (D.4)). The asymptotic value of the incomplete beta function for given q in the limit n → ∞ is indicated through dotted lines. The filled circle corresponds to a power n = 3 and an overdensity of a critical stable sphere.