A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms

The Abramov-Petkovsek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We modify the Abramov-Petkovsek reduction so as to decompose a hypergeometric term as the sum of a summable te...

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Bibliographic Details
Main Authors Chen, Shaoshi, Huang, Hui, Kauers, Manuel, Li, Ziming
Format Journal Article
LanguageEnglish
Published 19.01.2015
Subjects
Computer Science - Symbolic Computation
Mathematics - Rings and Algebras
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Summary:The Abramov-Petkovsek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We modify the Abramov-Petkovsek 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-Petkovsek 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.
DOI:10.48550/arxiv.1501.04668