Finding Differential Transform Using Difference Equations

Differential transform is applied to solve linear and nonlinear ordinary differential/difference equations. Many properties of the differential transform are known. In this paper, we construct and prove new properties of the differential transform. We particularly look into the differential transform of certain quotients of functions. Also, we construct and prove interesting relations between the differential transform, the difference operator, and incomplete gamma functions. Finally, we present some numerical examples to illustrate the results.