On the Gosper-Petkovsek Representation of Rational Functions

William Y. C. Chen and Husam L. Saad

  Abstract:   We show that the uniqueness of the Gosper-Petkov·sek representation of rational func- tions can be utilized to give a simpler version of Gosper's algorithm. This approach also applies to Petkov·sek's generalization of Gosper's algorithm, and its q-analogues by Abramov-Paule-Petkov·sek and BÄoing-Koepf.

  Keywords:  Gosper's algorithm, GP representation, q-Gosper's algorithm, q-GP repre- sentation, hypergeometric term.