By Bruno Salvy
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums or integrals by synthesizing summands or integrands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite sums or integrals of D-finite functions as well as the associated certificates in a compact form. In the integral case, the algorithm relies on a generalization of the Hermite reduction in symbolic integration. In the sum case, the algorithm relies on a discrete analogue of the generalized Hermite reduction, or equivalently, a generalization of the Abramov-Petkovsek reduction. We present a Maple implementation with good timings on a variety of examples.
By Christian Krattenthaler
By Christian Krattenthaler
By Christian Krattenthaler
By Christian Krattenthaler
By Bruno Salvy
By Marni Mishna
By Marc Mezzarobba
By Alain Connes
By Marc Moreno Maza
By Marc Moreno Maza
By Christoph Koutschan
By Christoph Koutschan
