Cored power-law density profile

A cored power-law density profile is finite at its centre and approaches a power law outside a core radius. A simple continuous example is $n(r)=n_0$ for $r\le r_c$ and $n(r)=n_0(r/r_c{)}^{-\beta }$ for $r>r_c$. The normalization $n_0$ is the core density. Smoothing the transition changes integrated coefficients but not convergence thresholds fixed by the outer slope.