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Powers of Distances on Unit Disk
Posted:
Jul 6, 1996 11:04 PM


Let A[n] denote the average of the nth powers of the distances between two points on a unit disk (radius=1). For example, the average of the squares of distances between two points on a unit disk is PI. The values of A[n] for the first few even values of n are listed below:
average of nth n powers of distances   2 PI 4 (5/3)PI 6 (7/2)PI 8 (42/5)PI 10 22 PI 12 ?
What is the general expression for A[n]?



