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{s}ek reduction. We provide a Maple implementation with good timings on a variety of examples.

翻译：创意伸缩法是由Zeilberger提出的一种算法方法，通过合成可伸缩的被加项（称为证书）来计算定和。我们描述了一种创意伸缩法算法，该算法能够计算D-有限函数定和的可伸缩项及其相关证书的紧凑形式。该算法基于广义Hermite约化的离散模拟，或等价于Abramov-Petkovšek约化的推广。我们提供了Maple实现，并在多种示例上展现出良好的运行时间性能。