Let $ S\in\mathcal S_N$ be a $ N\times N$ symmetric matrix over the reals, and introduce the (normalised) gaussian measure $ $ \mathrm d\mu(S):=2^{-\frac 12N}\pi^{-\frac14N(N+1)}\exp\left[-\frac12\operatorname{tr}(S^2)\right]\mathrm dS $ $ where $ $ \mathrm dS:=\prod_{i\le j\le N}\mathrm dS_{ij} $ $ I am interested in the integral $ $ p_n(N):=\int_{\mathcal S_N}\operatorname{tr}(S^{2n})\mathrm d\mu(S) $ $ which is in factRead more