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

Speaker: Dr. Frederic Chyzak
        (INRIA Saclay, France)

Time and Location: Wednesday, December 9, 2020, 14:30 p.m.
                   Zoom link: https://jku.zoom.us/j/93586556252


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. In this talk, we extend Hermite reduction to arbitrary linear
differential operators instead of the pure derivative, and develop
efficient algorithms for this reduction. We also 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. Based on joint work
with A. Bostan, P. Lairez, and B. Salvy.