On the Gosper-Petkovšek representation of rational functions

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