Wed Mar 13 10:47:37 EDT 2013

Tailor series

I need (numerical) Tailor series for formulas like:

       ( exp(P0) / p0 ) ^ 1/N

How to express this?  Essentially this is just convolution.  The
trouble is to be careful with numerical instabilities, so it might be
good to keep some form of symbolic computation going, e.g. don't add 1
to a small number e , but keep track of 1 + e such that subsequent - 1
is still precise.

The trick here is probably to use lazy sequences.  However, that seems
like a pain to implement.  Or not?

EDIT: Representing series as functions on natural numbers seems like a
good idea.  All primitive series are simple functions, and any
numerical series could be represented as a function also.