Weird integral

  • Thread starter mhill
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Main Question or Discussion Point

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 ?
 

Answers and Replies

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

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