Baker–Campbell–Hausdorff formula

In mathematics, the Baker–Campbell–Hausdorff formula gives the value of Z {\displaystyle Z} that solves the equation e X e Y = e Z {\displaystyle e^{X}e^{Y}=e^{Z}} for possibly noncommutative X and Y in the Lie algebra of a Lie group. There are various ways of writing the formula, but all ultimately yield an expression for Z {\displaystyle Z} in Lie algebraic terms, that is, as a formal series (not necessarily convergent) in X {\displaystyle X} and Y {\displaystyle Y} and iterated commutators thereof.

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