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I would very much appreciate any suggestions and/or pointers to references relevant for the analytic evaluation of the following n-dimensional iterated integral $$\int_{-\infty}^{+\infty}dx_1\int_{-\infty}^{x_1}dx_2\ldots\int_{-\infty}^{x_{n-1}}dx_n f(x_1)f(x_2)\ldots f(x_n)$$ where $$f(x_k) = \exp [i a_k x_k^2 +i b_k x_k]$$ and $a_k$, $b_k$ are arbitrary non-zero real numbers, and $i^2 = -1$.

I would very much appreciate any suggestions and/or pointers to references relevant for the analytic evaluation of the following n-dimensional iterated integral $$\int_{-\infty}^{+\infty}dx_1\int_{-\infty}^{x_1}dx_2\ldots\int_{-\infty}^{x_{n-1}}dx_n f_1(x_1)f_2(x_2)\ldots f_n(x_n)$$ where $$f_k(x_k) = \exp [i a_k x_k^2 +i b_k x_k]$$ and $a_k$, $b_k$ are arbitrary non-zero real numbers, and $i^2 = -1$.