@inproceedings{BoSaSc08, author = {Bostan, Alin and Salvy, Bruno and Schost, {\'E}ric}, title = {Power Series Composition and Change of Basis}, booktitle = {ISSAC'08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation}, year = {2008}, editor = {Jeffrey, David J.}, publisher = {ACM Press}, pages = {269--276}, doi = {10.1145/1390768.1390806}, arxiv = {abs/0804.2337}, 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.}, }