I am trying to decide when a function can be written as a Taylor series. I think it exists if the following condition is met:
For a Taylor series of $f(x)$ about the point $a$
In the region $R$ containing both $x$ and $a$, the function $f(x)$ is single-valued with an infinite number of continuous derivatives that all exist.
Is this both a necessary and sufficient condition? If not then what is?