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Power Series Composition and Change of Basis

Abstract : Efficient algorithms are known for many operations on truncated power series (multiplication, powering, exponential, ...). Composition is a more complex task. We isolate a large class of power series for which composition can be performed efficiently. We deduce fast algorithms for converting polynomials between various bases, including Euler, Bernoulli, Fibonacci, and the orthogonal Laguerre, Hermite, Jacobi, Krawtchouk, Meixner and Meixner-Pollaczek.
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https://hal.inria.fr/inria-00273385
Contributor : Bruno Salvy <>
Submitted on : Tuesday, April 15, 2008 - 11:18:32 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Friday, May 21, 2010 - 1:45:11 AM

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  • HAL Id : inria-00273385, version 1
  • ARXIV : 0804.2337

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Alin Bostan, Bruno Salvy, Éric Schost. Power Series Composition and Change of Basis. ISSAC'08 : International Symposium on Symbolic and Algebraic Computation, Jul 2008, Hagenberg, Austria. ⟨inria-00273385⟩

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