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arXiv · 2608.05053

A variation of Eichler's proof of the Baker-Campbell-Hausdorff formula

Eugene Ha
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Abstract

Eichler gave an elementary but involved proof of the Baker-Campbell-Hausdorff formula, based on the associativity of the product of three exponentials. We show that by considering the associativity of the product of four exponentials, one can bypass the complications of Eichler's proof to arrive at a shorter proof that is both elementary and straightforward. As a corollary of the proof, a recursive scheme for the Baker-Campbell-Hausdorff formula is derived, in which explicit Bernoulli numbers are notably absent.

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Eugene Ha. 2026-08-05. A variation of Eichler's proof of the Baker-Campbell-Hausdorff formula. https://arxiv.org/abs/2608.05053

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