幂级数的合成与基的变换
Power Series Composition and Change of Basis
摘要：
已知有效算法用于截断幂级数上的许多运算（乘法、幂、指数等）。写作是一项更复杂的任务。我们隔离了一大类的幂级数的组成，可以有效地进行。我们推导出快速算法转换多项式之间的各种基地，包括欧拉，伯努利，斐波那契，和正交Laguerre，厄米，雅可比，Krawtchouk，Meixner和Meixner-Pollaczek。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
