I have found many references to Poincaré and Borel in relation to their work on asymptotic series, but so far, every source I can get my hands on is very old, hence hard to read (this is not true in general, but in this case, texts that predate Oh notation tend not to be clear).



> 
> Can you explain the idea behind asymptotic series, give an illuminating example, and/or suggest a good modern exposition of the theory?
> 
> 
> 



Asymptotic series
Web pages of



> 
> Michael Berry: <http://www.phy.bris.ac.uk/people/berry_mv/dingle.html>
> 
> 
> 


and



> 
> John Boyd: <http://www-personal.umich.edu/~jpboyd/>
> 
> 
> 


both include helpful published and publicly available sources. 


