Let $f$ be a holomorphic function with multiple variables.
$f: {\mathbb C}^n \to {\mathbb C}$
Does $f$ have an infinite radius of convergence for its Taylor series?
If so, is the function equal everywhere to its Taylor series?
I think the convergence of Taylor series could be extended from this 1D case. But I'm not sure how to give a formal prove whether it's equal to the original function or not.
Thank you.