Is There a Generalization of the Gaussian Integral for Quartic and Higher Terms?

[mhill]

if we had that A_{i,j,k,l} is a set of number could we obtain for the integral

\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}

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 ?

 

[mathman]

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