  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.
