For teaching purposes I'd need a continuous function of a single variable that is "difficult" to approximate with polynomials, i.e. one would need very high powers in a power series to "fit" this function well. I intend to show my students the "limits" of what can be achieved with power series.
I thought about concocting something "noisy", but instead of rolling my own I am just wondering whether there is a kind of standard "difficult function" that people use for testing approximation / interpolation algorithms, somewhat similarly to those optimisation test functions that have numerous local minima where naive algorithms get stuck easily.
Apologies if this question is not well-formed; please have mercy on a non-mathematician.