arXiv Open Access 2023

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

Hadrien Brochet Bruno Salvy

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Abstrak

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.

Topik & Kata Kunci

cs.SC

Penulis (2)

Hadrien Brochet

Bruno Salvy

Format Sitasi

APA MLA BibTeX

Brochet, H., Salvy, B. (2023). Reduction-Based Creative Telescoping for Definite Summation of D-finite Functions. https://arxiv.org/abs/2307.07216

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓