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.