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Topic: Powers of Distances on Unit Disk
Replies: 2   Last Post: Jul 7, 1996 3:24 PM

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Kevin Brown

Posts: 31
Registered: 12/12/04
Powers of Distances on Unit Disk
Posted: Jul 6, 1996 11:04 PM
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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]?







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