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I am trying to evaluate $\int_\phi e^{tr(RM)} dR$ where $\phi$ is a set of all real orthogonal matrices of a certain size. $M$ is an arbitrary real matrix (of a certain size). This is equivalent to $$\...

I posted this question previously to MathSE. However, I have still not solved it, so lets try to ask it here. When doing some calculations with spin-foam models for 3d quantum gravity for some ...

Consider the following integral, $$ {1 \over 4\pi^{2}}\int_{0}^{2\pi}\int_{0}^{2\pi} \sqrt{\, 9 -\sin^{2}\left(\theta_{1} \over 2\right) \sin^{2}\left(\theta_{2} \over 2\right)\,} \,{\rm d}...