= Mestel disk potential-density pair
{c}
{title2=$\Phi=v_0^2\log[(r+|z|)/R_*]$}
The reflection-symmetric <Newtonian gravitational potential> $\Phi=v_0^2\log[(\sqrt{R^2+z^2}+|z|)/R_*]$ is harmonic off the plane. Its normal-derivative jump is $2v_0^2/R$, so the <Poisson equation for Newtonian gravity> gives <surface density of a disk> $S=v_0^2/(2\pi GR)$ and volume <mass density> $\rho=S\delta(z)$. The midplane <circular speed> is constant. The scale-free model has infinite total <mass> and does not use a finite-mass boundary condition at infinity.
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