The ideal resonance problem a comparison of two formal solutions III

This is the last article in a series of the same title. The two formal solutions of the Ideal Resonance Problem, developed respectively by Garfinkel and Jupp, were compared and contrasted in the earlier papers. It was stated there that the principal shortcoming of Jupp's analytical solution was the occurrence of a singularity at the separatrix. The purpose of this contribution is to demonstrate how this singularity may readily be removed. Accordingly, modified solutions are presented for the libration and circulation regions.