Baker-Campbell-Hausdorff formula

The Baker-Campbell-Hausdorff (BCH) formula provides a solution for Z in the equation

eXeY=eZ

where X and Y are possibly noncommutative elements in the Lie algebra of a Lie group.
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The formula itself is an infinite series expansion:

log(eXeY)=X+Y+12[X,Y]+112([X,[X,Y]]+[Y,[Y,X]])+

Related: Zassenhaus formula.