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Pré-Publication, Document De Travail Année : 2023

Reduction-Based Creative Telescoping for Definite Summation of D-Finite Functions

Résumé

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-Petkovšek reduction. We provide a Maple implementation with good timings on a variety of examples.
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hal-04295759 , version 1 (20-11-2023)

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Hadrien Brochet, Bruno Salvy. Reduction-Based Creative Telescoping for Definite Summation of D-Finite Functions. 2023. ⟨hal-04295759⟩
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