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
.