What is Lane Emden Equation?

Lane Emden Equation is this ordinary differential equation.

The "$\xi$" is independence variable and means radius of a star. The "$\theta$" is a function depend on $\xi$. The value of $\theta$ equals 1 in the center of the star, and equals 0 in the surface. The "$n$" is a parameter that characterizes the equation and called polytropic index.
Lane Emden Equation is very important for astrophysics. If you want to know details of this, please see Wikipedia!

calculation

Please input polytropic index $n$. You can get the value of $\xi$ such as $\theta(\xi) = 0$.

Input value of $n$

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