Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
arXiv:1805.03445 · doi:10.1145/3208976.3208992
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.
Accepted for publication in the proceedings of the conference ISSAC'18 (Jul 16-19, 2018)