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How to get this gaussian integral result?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125808] How to get this gaussian integral result?
  • From: simplerbysimpler at gmail.com
  • Date: Tue, 3 Apr 2012 04:49:41 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

 Integrate[
 x1^(n1) x2^(n2)  x3^(n3) Exp[
   a x1 x1 + b x2 x2 + c x3 x3 + d12 x1 x2 + d23 x2 x3 + d13 x1 x3 +
    d], {x1, -Infinity, Infinity}, {x2, -Infinity,
  Infinity}, {x3, -Infinity, Infinity}].  n1,n2,n3 are Natural numbers.  I still cannot get the general result ,although mathematica takes so much time. Can you help me about this?



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