An Improved Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms

The Abramov-Petkovšek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We modify the AbramovPetkovšek reduction so as to decompose a hypergeometric term as the sum of a summable term and a non-summable one. The outputs of the Abramov-Petkovšek reduction and our modified version share the same required properties. The modified reduction does not solve any auxiliary linear difference equation explicitly. It is also more efficient than the original reduction according to computational experiments. Based on this reduction, we design a new algorithm to compute minimal telescopers for bivariate hypergeometric terms. The new algorithm can avoid the costly computation of certificates.