Can anyone provide an example of a real-valued function *f* with a convergent Taylor series that converges to a function that is not equal to *f* (not even locally)?



What's an example of a function whose Taylor series converges to the wrong thing?
If you take the classic non-analytic smooth function: $e^{-1/t}$ for $t \gt 0$ and $0$ for $t \le 0$ then this has a Taylor series at $0$ which is, err, $0$. However, the function is non-zero for any positive number so it does not agree with its Taylor series in any neighbourhood of $0$.


