Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series

The infinite series for log(exp X exp Y) for noncommuting X and Y is expressible in terms of iterated commutators of X and Y except for the linear term X+Y. Dynkin derived an explicit expression for the terms as a sum of iterated commutators over a certain set of sequences. This paper presents a practical algorithm for applying Dynkin’s formula and gives several illustrative examples.