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

Author:

Hadrien Brochet, Bruno Salvy

Keyword:

Computer Science, Symbolic Computation, Symbolic Computation (cs.SC)

journal:

date:

2023-07-13 16:00:00

Abstract

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.

PDF: Reduction-Based Creative Telescoping for Definite Summation of D-finite Functions.pdf