help with an integral

• To: mathgroup at smc.vnet.net
• Subject: [mg5310] help with an integral
• From: "Dimitris Agrafiotis" <dimitris at 3dp.com>
• Date: Sat, 23 Nov 1996 01:44:46 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```I have a rather complicated integral to compute and I was wondering if
Mathematica can help me do it. Unfortunately, I don't have access to
this package. The integral is as follows:

+inf
S = -integral(p(x) ln(p(x)))
-inf

where
n
p(x) = (1/a) * SUM(exp^-((x - c(i))^2 / b)
i=1

and a, b, and c(i) are constants. p(x) is essentially a sum of
n Gaussians, each centered at its own c(i). x and c(i) are d-
dimensional vectors. Can the integral be computed/approximated,
and if so, how many dimensions can we handle? How about the
sample size, n (i.e. the number of Gaussians)? Can that be
arbitrarily large?

Your help would be greatly appreciated. Thanks,

--
Dimitris K. Agrafiotis, PhD              | e-mail: dimitris at 3dp.com
3-Dimensional Pharmaceuticals, Inc.      | tel:    (610) 458-6045
665 Stockton Drive, Suite 104            | fax:    (610) 458-8249
Exton, PA 19341

```

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