Editing Stellar dynamics (section)

=== Surface density and mass of a thick disk ===

Integrating over the entire thick disc of uniform thickness <math> 2 z_0 </math>, we find the surface density and the total mass as 
<math display="block"> \Sigma(R) = (2 z_0)\rho(R,0), ~~ M_0 = \int_0^\infty (2\pi R dR) \Sigma(R). </math>

This confirms that the absence of extra razor thin discs at the boundaries.  In the limit, <math> z_0 \rightarrow 0 </math>, this thick disc potential reduces to that of a razor-thin Kuzmin disk, for which we can verify <math>{|g_z (R,0+)| \over 2\pi G} \rightarrow \Sigma(R) \rightarrow {M_0 R_0 \over 2\pi (R^2+R_0^2)^{3/2}} </math>.