The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) | = | integral_0^1 ... integral_0^1_︸_n sqrt(x_1^2 + ... + x_n^2)d x_1 ...d x_n | = | s/(Γ(1 - 1/2 s)) integral_0^∞ (1 - [b(u)]^n)/u^(s + 1) where r is the distance and b(u) | = | integral_0^1 e^(-u^2 x^2) d x | = | (sqrt(π)erf(u))/(2u)

box integral | cube point picking | hypercube line picking | line point picking | square point picking