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A convergent $1/n$-expansion for GSE and GOE
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We generalize the results on the asymptotic expansion from Gaussian Unitary Ensembles case to all Gaussian Ensembles. We derive differential equations on densities and their moment generating functions for all Gaussian Ensembles. Also, we calculate explicit expressions for the moment generating functions for all Gaussian Ensembles.
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Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
The spectral densities of the Gaussian, Laguerre, and Jacobi β-ensembles satisfy explicit linear differential equations of order β+1, derived uniformly for β=2,4 (and Gaussian β=6,2/3).
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