Having no prior exposure to several complex variables, I am trying to read some papers involving this subject. I came upon the terms analytic polynomial and holomorphic polynomial. Do they simply refer to every polynomial on $N$ complex variables? And if so, why the extra emphasis?
Note: I found a related question for one complex variable here and I suspect the answer to be the same, but I just wanted to make sure I don't miss anything.
EDIT: Example of use:
Lemma Let $K_1$, $K_2$ be two disjoint compact convex subsets of $\mathbb{C}^n$. Then any holomorphic function $h$ on an open set $V \supset K_1 \cup K_2$ can be uniformly approximated on $K_1 \cup K_2$ by analytic polynomials.