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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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).