Power series composition and change of basis

Authors:
Alin Bostan;Bruno Salvy;Éric Schost
Affiliations:
INRIA, Rocquencourt, France;INRIA, Rocquencourt, France;University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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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.