= Jeans moments from an augmented density
{c}
{title2=$A=\int_0^\psi\rho\,dq,\quad B=A+\tfrac r2\partial_rA$}
With radial pressure zero at $\psi=0$, an <augmented density> supplies $\rho\langle v_r^2\rangle=\int_0^\psi\rho(r,q)dq$ and $\rho\langle v_\theta^2\rangle=(2r)^{-1}\int_0^\psi\partial_r[r^2\rho(r,q)]dq$. The derivative holds $q$ fixed. Their chain-rule combination satisfies the <Spherical Jeans equation>, but the physical density alone does not choose an augmented extension.
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