Approximate analytical solutions of the Lane–Emden equation for a self-gravitating isothermal gas sphere

The isothermal Lane–Emden equation arises in many astrophysical problems, in particular in modelling of a self-gravitating, polytropic gas in a spherically symmetric configuration. In this work, the isothermal Lane–Emden equation is investigated using the fractional approximation technique. The method provides an efficient and accurate way of obtaining approximate analytic solution to the Lane–Emden equation thus is useful in the modelling of self-gravitating gaseous spheres in astrophysics.