Rofe-Beketov’s formula on time scales

We establish the Rofe-Beketov formula for the second order Sturm–Liouville dynamic equation on time scales. This formula shows how to express a second linearly independent solution of this equation if one solution is known. In contrast to the D’Alembert formula (sometimes also called the reduction of order formula), no restriction on the oscillatory behavior of the known solution is needed.