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Some “Short” Proofs of the CBHD Theorem

  • Andrea BonfiglioliEmail author
  • Roberta Fulci
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2034)

Abstract

THE aim of this chapter is to give all the details of five other proofs (besides the one given in Chap. 3) of the Campbell, Baker, Hausdorff Theorem, stating that ; xy := Log(Exp(x) ·Exp(y)) is a series of Lie polynomials in x, y. As we showed in Chap. 3, this is the “qualitative” part of the CBHD Theorem, and the actual formula expressing xthat xy as an explicit series (that is, Dynkin’s Formula) can be quite easily derived from this qualitative counterpart as exhibited in Sect. 3.3.

Keywords

Associative Algebra Formal Power Series Recursion Formula Bernoulli Number Topological Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly

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