A First Course in Complex Analysis · Problem 8.4.6

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis

Problem

Show that Corollary 8.1.10 is false when translated to

\mathbb{R}

. That is, find a real analytic function

f: \mathbb{R} \to \mathbb{R}

and a point

x_0 \in \mathbb{R}

such that the radius of convergence of the power series expansion of

f

x_0

is strictly less than the distance from

x_0

to the boundary of the domain of

f