Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions - Archive ouverte HAL Access content directly
Conference Papers Year : 2018

Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

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Alin Bostan
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  • PersonId : 831654
Pierre Lairez
Bruno Salvy

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.
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Dates and versions

hal-01788619 , version 1 (09-05-2018)

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Cite

Alin Bostan, Frédéric Chyzak, Pierre Lairez, Bruno Salvy. Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions. ISSAC 2018 - International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.1-8, ⟨10.1145/3208976.3208992⟩. ⟨hal-01788619⟩
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