I would like to know how are encoded the real-analytic functions on the interval by the computers. When I think in a real-analytic function I just think in a composition of the ''typical'' analytic functions of every day, in all of this cases it is possible to find an ''exact''(because there is an explicit formula for the taylor expansion at any point) representation of these functions. I want also to ask if someone could give an example of a real-analytic function for which the representation in a computer is very bad behaves.



How are real-analytic functions encoded in computer algebra?
The function $\sum \frac{x^n}{n^n}$ has been [discusssed](https://mathoverflow.net/questions/109160). Other choices for the denominator might also give convergent functions defined by power series whose behavior is complicated. Maybe that is relevant.


