Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2001 • Question 6

Question

Math 6210 • Real Analysis 2001 • Question 6

Suppose that \(f\) is holomorphic in the open disc of radius \(r\), centered at \(z_0\), but does not have an analytic extension to any neighborhood of the closure of this disc. Show that the radius of convergence of the power series expansion for \(f\) centered at \(z_0\) is \(r\).

Raw LaTeX

Suppose that \(f\) is holomorphic in the open disc of radius \(r\),
centered at \(z_0\), but does not have an analytic extension to any neighborhood
of the closure of this disc. Show that the radius of convergence of the power
series expansion for \(f\) centered at \(z_0\) is \(r\).

Topic Tags

Almost Everywhere and Convergence in Measure Convergence Theorems Holomorphic Functions and Cauchy-Riemann Equations Weak Topologies and Weak Convergence