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Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
Abstract : Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite reduction to arbitrary linear differential operators instead of the pure derivative, and develop efficient algorithms for this reduction. We then apply the generalized Hermite reduction to the computation of linear operators satisfied by single definite integrals of D-finite functions of several continuous or discrete parameters. The resulting algorithm is a generalization of reduction-based methods for creative telescoping.
Cited literature [45 references]
https://hal.inria.fr/hal-01788619
Contributor : Frédéric Chyzak Connect in order to contact the contributor
Submitted on : Wednesday, May 9, 2018 - 11:39:00 AM
Last modification on : Thursday, January 20, 2022 - 4:13:59 PM
Long-term archiving on: : Tuesday, September 25, 2018 - 7:03:15 PM
Contributor : Frédéric Chyzak Connect in order to contact the contributor
Submitted on : Wednesday, May 9, 2018 - 11:39:00 AM
Last modification on : Thursday, January 20, 2022 - 4:13:59 PM
Long-term archiving on: : Tuesday, September 25, 2018 - 7:03:15 PM
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