Lane-Emden function (${\theta }_n(\xi )$)

The regular dimensionless solution of the Lane-Emden equation with ${\theta }_n(0)=1$ and ${\theta }_n^{\prime }(0)=0$. 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 $-{\xi }_1^2{\theta }_n^{\prime }({\xi }_1)$ specify radius and mass factors for the corresponding finite-radius stellar polytrope.