Accelerated power series solution of polytropic and isothermal gas spheres

In this paper, a power series solution for the Lane-Emden equation has been developed. We construct a recurrence relation for the coefficients a(k) in the power series expansion theta(x) = Sigma a(k)x(k) of the solution of the Lane-Emden equation. For a polytrope with index n less than or equal to 1.9 the series appear to converge everywhere inside the star. For n > 1.9 the series converges in the inner radii, but then diverges. To improve the convergence radii of the series we used a combination of two accelerating techniques, Euler-Abel transformation and Pade approximation. These transformed series converge everywhere for n less than or equal to 5. A comparison with the isothermal sphere reveals a good fit with both the numerical and four terms optimized model developed by Hunter [MNRAS 328 (2001) 839]. (C) 2004 Elsevier B.V. All rights reserved.