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Hypervirial Models of Stellar Systems by N. W. Evans and J. An (2005, 10.1111/j.1365-2966.2005.09078.x)

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Monthly Notices of the Royal Astronomical Society 360, pp.492–498. Section 2.2, equations(18)–(20), derives the power-law constant-anisotropy density and moments with explicit integrability conditions.
arxiv.org/html/astro-ph/0501091

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