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Weird integral

  1. Apr 23, 2008 #1
    if we had that [tex] A_{i,j,k,l} [/tex] is a set of number could we obtain for the integral

    [tex] \int_{-\infty}^{\infty} dV e^{-A_{i,j,k,l}x^{i}x^{j}x^{k}x^{l}} = C |A_{i,j,k,l}|^{-b} [/tex]

    here C and b are real constant, i am looking for a quartic or similar analogue to Gaussian integral, but can be defined as a generalization to the usual Gaussian integral for quartic and further terms ?
  2. jcsd
  3. Apr 23, 2008 #2


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    Science Advisor

    Your integrand looks like the joint density function for 4 correlated Gaussian random variables. There is nothing special about 4.
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