Radial Oscillations of Stellar Models: Density Distributions which Lead to Three-term Recurrence Relations

In an early paper Sterne investigated the pulsational properties of three stellar models with specified density distributions. He assumed a solution for the relative amplitude of the displacement to be of the form [IMAGE] and on substitution into Eddington’s equation for small radial adiabatic oscillations of a star [IMAGE] obtained a two-term recurrence relation to solve for the a_n in the case of each model.