# Integration of exponentials of quadratic forms (general Gaussian itegrals) over semi-finite domains

Hi

I'm interested in evaluating the integral of $e^{-s^T A s + b s}$ over a semi-infinite domain. $A$ is $\binom{N}{2}$x$\binom{N}{2}$ and has $N-1$ eigenvalues equal to $N$, and the rest 0. In particular, how does one deal with the limits of integration under an orthogonal transformation of the variables?

Deepak

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Integral over what? (Please define your semi-infinite domain.) Also I have a hanging suspicion that your question will be better received at math.stackexchange.com –  Willie Wong Jan 24 '11 at 19:23
And as far as I know, $-a^TAs+bs$ is not a quadratic form... –  David Roberts Jan 24 '11 at 23:44