I think that a significant part of the difficulties in the discussions
about Taylor series and the like has been the lack of a common and
unambiguous vocabulary. So, I've started a wiki page defining some
concepts in order to clarify things:
https://github.com/sympy/sympy/wiki/Function-expansions
Feel free to expand or amend it, add links to and from it, etc.
NB: I had to use Markdown syntax because I couldn't figure out how to
get LaTeX to work in rST.

Also while writing it, I've noticed 2 additional problems with
Expr.series:
* The order is off by one.
* Its name is misleading since it doesn't return a series. 

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