The expected value 
of 
from a fixed vertex of a unit 
-cube to a point picked at random in the interior of the hypercube is given by
 |  |  | (1) |
 |  | ![s/(Gamma(1-1/2s))int_0^infty(1-[b(u)]^n)/(u^(s+1))](https://mathworld.wolfram.com/images/equations/HypercubePointPicking/Inline9.svg) | (2) |
where 
is the distance and
 |  |  | (3) |
 |  |  | (4) |
(Bailey et al. 2006).
The first few values of expected distances 
are given by
 |  |  | (5) |
 |  |  | (6) |
 |  |  | (7) |
 |  |  | (8) |
where the term
 |  |  | (9) |
 |  |  | (10) |
is not known in closed form (Bailey et al. 2006; Bailey et al. 2007, pp. 238 and 272).
It is related to the expected distance from the center of the unit 
-cube by
 | (11) |
(Bailey et al. 2006).
