# Explicit Baker–Campbell–Hausdorff Expansions

School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand

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Current address: Research Institute of Mathematical Sciences, Kyoto University, Sakyo Ward, Kyoto, Kyoto Prefecture 606-8317, Japan

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Author to whom correspondence should be addressed.

Received: 20 July 2018 / Revised: 5 August 2018 / Accepted: 6 August 2018 / Published: 8 August 2018

# Abstract

The Baker–Campbell–Hausdorff (BCH) expansion is a general purpose tool of use in many branches of mathematics and theoretical physics. Only in some special cases can the expansion be evaluated in closed form. In an earlier article we demonstrated that whenever*Keywords:*Lie algebras; matrix exponentials; matrix logarithms; Baker–Campbell–Hausdorff (BCH) formula; commutators; creation-destruction algebra; Heisenberg commutator

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**MDPI and ACS Style**

Van-Brunt, A.; Visser, M. Explicit Baker–Campbell–Hausdorff Expansions. *Mathematics* **2018**, *6*, 135.

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