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