Computing the coefficients for the power series solution of the Lane-Emden equation with the Python library SymPy

It is shown how the Python library Sympy can be used to compute symbolically the coefficients of the power series solution of the Lane-Emden equation (LEE). Sympy is an open source Python library for symbolic mathematics. The power series solutions are compared to the numerically computed solutions using matplotlib. The results of a run time measurement of the implemented algorithm are discussed at the end. Derivation of the recurrence formulas for the coefficients of the power series solution of the LEE In stellar physics the LEE is a second order nonlinear ordinary differential equation (ODE) which describes the internal state of a gaseous polytrophic sphere of index , for details see reference (1), chapter 4. The LEE reads as follows: (1) ( ( )) [ ( )] or