Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite sums of D-finite functions as well as the associated certificates in a compact form. The algorithm relies on a discrete analogue of the generalized Hermite reduction, or equivalently, a generalization of the Abramov-Petkov\v sek reduction. We provide a Maple implementation with good timings on a variety of examples.

翻译：创造型 telescoping 是由 Zeilberger 提出的一种算法方法，通过合成可 telescoping 的和项（称为证书）来计算确定和。本文描述了一种创造型 telescoping 算法，该算法以紧凑形式计算 D-有限函数确定和的 telescoper 及相关证书。该算法基于广义 Hermite 约化的离散类似形式，或等价地，Abramov-Petkovšek 约化的推广。我们提供了 Maple 实现，并在多种示例上取得了良好的运行时间表现。