From: Joe Keane <jgk@jgk.org>
Newsgroups: sci.math
Subject: distance in n-cube
Date: 29 Nov 1996 21:04:58 -0800
Message-ID: <57of9q$ia9@shellx.best.com>

So i've been browsing through Steven Finch's site about constants
<A HREF="http://www.mathsoft.com/asolve/constant/constant.html">
Favorite Mathematical Constants</A>.  It is most interesting.

One page has comments about Delta(n), the expected distance between two
points in an n-cube.  It asks about the asympotics, so i came up with a
rather lengthy derivation to get an asymptotic formula for Delta(n):

        Delta(n) ~ sqrt(1/6*n) * { 1 - 7/40 * n^-1 - 65/896 * n^-2 -
            3023/179200 * n^-3 + 48280227/315392000 * n^-4 + ... }

I'm pretty sure of the result, but my method is rather convoluted.  I'd
like to know if anyone has a reference, proof, refutation, or whatever.

Another interesting question is whether Delta(n) can always be expressed
in terms of elementary functions; i think that it may be true.

--
Joe Keane, amateur mathematician