Lane-Emden function
= Lane-Emden function
{c}
{title2=$\theta_n(\xi)$}
The regular dimensionless solution of the <Lane-Emden equation> with $\theta_n(0)=1$ and $\theta_n'(0)=0$. Its local expansion is $\theta_n(\xi)=1-\xi^2/6+n\xi^4/120+O(\xi^6)$. If it has a first zero $\xi_1$, that zero and $-\xi_1^2\theta_n'(\xi_1)$ specify radius and <mass> factors for the corresponding finite-radius <stellar polytrope>.