Incomplete beta function Iξ(a,b) (black contours) for a = (n − 1)/2 and b = 1/2 as function of ξ = 1 − yn. 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 = q2 /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.
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