A sequence of E-type composite analytical solutions of the Lane-Emden equation

A sequence of new E-type composite analytical solutions to the Lane-Emden equation, based on the indices zero and one, has been developed which eliminates the arbitrary character of the physical radius of the polytropic stellar model due to the surface density condition Q = O never being satisfied. The polytropic models associated with the presented solutions have a large central uniform density n = O zone matched, in a physically consistent way, to a small outer n = 1 zone which has a steep density gradient giving Q = O, along with T = O and P = O, at the radial distance corresponding to the first zero of the composite solution.