We consider a series expansion around θ θ = 0 θ θ = ∑ ∑ m = 0 ∞ ∞ a m ξ ξ m with initial values θ θ | ξ ξ = 0 = θ θ 0 and d θ θ d ξ ξ | ξ ξ = 0 = 0 . Plugging this into the Lane-Emden equation, we can show that all odd coefficients of the series vanish a 2 m + 1 = 0 . Furthermore, we obtain a recursive relationship between the even coefficients b m = a 2 m of the series. b m + 1 = − − 1 ( 2 m + 2 ) ( 2 m + 3 ) ∑ ∑ k = 0 m b m − − k b k It was proven that this series converges at least for ξ ξ ≤ ≤ 1 but numerical results showed good agreement for much larger values.