Section: New Results

Generalized Hermite reduction, creative telescoping and definite integration of D-finite functions

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. Alin Bostan, Frédéric Chyzak, and Pierre Lairez, together with Bruno Salvy (project-team AriC) have extended Hermite reduction to arbitrary linear differential operators instead of the pure derivative. They have also developped efficient algorithms for this reduction, and then applied 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. Their article [6] was published at the ISSAC conference.