Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2016 • Question 7

Question

Math 6210 • Real Analysis Summer 2016 • Question 7

Let \(f(z)\) be analytic in a deleted neighborhood of \(z=a\) and \[ \lim _{z\to a}(z-a)f(z)=0. \] Does it mean that \(f(z)\) has a removable singularity at \(a\)? If so, prove it. If not, give a counterexample.

Raw LaTeX

Let \(f(z)\) be analytic in a deleted neighborhood of \(z=a\) and
\[
\lim_{z\to a}(z-a)f(z)=0.
\]
Does it mean that \(f(z)\) has a removable singularity at \(a\)? If so, prove it.
If not, give a counterexample.

Topic Tags

Analytic Continuation and Monodromy Isolated Singularities and Residues