Can anybody please tell me, how to evaluate a multivariate integral with a gaussian weight function. $$\int_{-\infty}^{\infty} \mathrm{d}x_{1}\,\mathrm{d}x_{2}\,\mathrm{d}x_{3}\,\mathrm{d}x_{4}\dots\,\mathrm{d}x_{n}\exp\left(\sum_{j}x_{j}^2\right)\times f(x_{1},x_{2},x_{3},x_{4}....x_{n})$$ where $$f(x_{1},x_{2},x_{3},x_{4}....x_{n})=\prod_{j} \frac{1}{\sqrt{(1+i\,k(x_{j}^2-x_{j+1}^2)^2)}}$$

I need a hint to solve this integral.

I have found that, I can relate this to a partition function $\mathcal{Z}$. Any ideas to solve this Integral?

This post imported from StackExchange Physics at 2014-03-06 21:15 (UCT), posted by SE-user Sijo Joseph