Pierre Lairez

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Équipe Specfun

email
INRIA Saclay Île-de-France, Bât. Alan Turing
1 rue Honoré d'Estienne d'Orves
Campus de l'École polytechnique
91120 Palaiseau
France
location
48.7146, 2.2056
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phone
(0033) 01 77 57 80 36
office
1155
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## Latest work

### Generalized Hermite reduction, creative telescoping and definite integration

2018

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.

$$\int_{-1}^{1}{\frac{e^{-px}T_n(x)}{\sqrt{1-x^2}}\,\mathrm{d} x}=(-1)^n\pi I_n(p)$$

A classical identity relating Chebyshev polynomials with Bessel functions