Power Series Composition and Change of Basis

Details Power Series Composition and Change of Basis Power Series Composition and Change of Basis

2008-04-15

arxiv.org/abs/0804.2337v1

Dans ISSAC'08 (2008)

Computer Science

Symbolic Computation

Scientific paper

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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