On the Gosper–Petkovšek representation of rational functions

We show that the uniqueness of the Gosper–Petkovšek representation of rational functions can be utilized to give a simpler version of Gosper’s algorithm. This approach also applies to Petkovšek’s generalization of Gosper’s algorithm, and its q-analogues by Abramov–Paule–Petkovšek and Böing–Koepf.