# Faster exponentials of power series

arXiv preprint (November 2009).

## Abstract

We describe a new algorithm for computing exp *f* where *f* is a power series in **C**[[*x*]]. If *M*(*n*) denotes the cost of multiplying polynomials of degree *n*, the new algorithm costs (2.1666... + *o*(1)) *M*(*n*) to compute exp *f* to order *n*. This improves on the previous best result, namely (2.333... + *o*(1)) *M*(*n*).

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