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Chebyshev Expansions for Solutions of Linear Differential Equations

Alexandre Benoit 1 Bruno Salvy 1
1 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
Abstract : A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.
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https://hal.inria.fr/inria-00395716
Contributor : Bruno Salvy <>
Submitted on : Tuesday, June 16, 2009 - 12:17:30 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Thursday, June 10, 2010 - 8:30:40 PM

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  • HAL Id : inria-00395716, version 1
  • ARXIV : 0906.2888

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Alexandre Benoit, Bruno Salvy. Chebyshev Expansions for Solutions of Linear Differential Equations. ISSAC'09, Jul 2009, Seoul, South Korea. ⟨inria-00395716⟩

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