Hypercube Point Picking

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)
			(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).

REFERENCES:

Bailey, D. H.; Borwein, J. M.; and Crandall, R. E. "Box Integrals." Preprint. Apr. 3, 2006.

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action.Wellesley, MA: A K Peters, 2007.