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Archive for History of Exact Sciences

, Volume 66, Issue 3, pp 295–358 | Cite as

The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin

  • Rüdiger Achilles
  • Andrea Bonfiglioli
Article

Abstract

The aim of this paper is to provide a comprehensive exposition of the early contributions to the so-called Campbell, Baker, Hausdorff, Dynkin Theorem during the years 1890–1950. Related works by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff, and Dynkin will be investigated and compared. For a full recovery of the original sources, many mathematical details will also be furnished. In particular, we rediscover and comment on a series of five notable papers by Pascal (Lomb Ist Rend, 1901–1902), which nowadays are almost forgotten.

Keywords

Transformation Group Fundamental Theorem Formal Power Series Bernoulli Number Noncommutative Algebra 
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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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