# Globally analytic function

From Calculus

## Definition

Consider a function defined on all of . We say that is **globally analytic** if it satisfies the following equivalent conditions:

- There is a point such that the Taylor series of at exists and converges to on all of .
- There is a point such that has a power series at that converges to on all of .
- For every point , the Taylor series of at exists and converges to on all of .
- For every point , has a power series at that converges to on all of .