Topics in Noncommutative Algebra pp 173-264 | Cite as

# Some “Short” Proofs of the CBHD Theorem

Chapter

First Online:

## 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 ; *x*♦*y :=* 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 *x*that *x*♦*y* 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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer-Verlag Berlin Heidelberg 2012