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arXiv · 0804.2337

Power Series Composition and Change of Basis

Alin Bostan·Bruno Salvy·Éric Schost
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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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Alin Bostan, Bruno Salvy, Éric Schost. 2008-04-15. Power Series Composition and Change of Basis. https://doi.org/10.1145/1390768.1390806

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