Power Series Composition and Change of Basis
Symbolic Computation
2013-06-19 v1
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.
Cite
@article{arxiv.0804.2337,
title = {Power Series Composition and Change of Basis},
author = {Alin Bostan and Bruno Salvy and Éric Schost},
journal= {arXiv preprint arXiv:0804.2337},
year = {2013}
}