Conditions must satisfy $f: (a, b) \to \mathbb{R}$ so that its Taylor series converge to f itself.

Question

I have a doubt.

What conditions must satisfy $f: (a, b) \to \mathbb{R}$ so that its Taylor series converge to f itself.

Answer 1

I am not sure what is exactly your question, but I think you look for $f$ being an analytic function. For example $$e^x= \sum_{k=0}^\infty \frac{x^k}{k!}$$ is analytic.