@techreport{RISC5102,author = {Shaoshi Chen and Hui Huang and Manuel Kauers and Ziming Li},
title = {{An Improved Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms}},
language = {english},
abstract = { 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 improve the Abramov-Petkovsek
reduction so as to decompose a hypergeometric term as the sum of a summable
term and a non-summable one. The improved 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.},
number = {1501.04668},
year = {2015},
institution = {arxiv},
length = {8}
}