There has been a sharp increase of research activities of the special Hill equation, the Whittaker-Hill equation in recent years. The Wh-equation is a second order linear Schrodinger type equation with an cosine potential. The WH-equation has a wide range of applications. We show how a complex analytic (Nevanlinna theory) approach can explain some recent results of Djakov and Mitaygin (2005) concerning the semifinite-gap problems of the Whittaker-Hill equation. Moreover, we have derived closed form solution of the WH-equation.