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))](/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).
