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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2011 • Question 9

Question

Math 6210 • Real Analysis Spring 2011 • Question 9

Find all isolated singularities of the function \[ f(z)=\sin (z)\sin \left (\frac {1}{z}\right ) \] in \(\mathbb C\). Determine the residues of \(f\) at these isolated singularities.

Raw LaTeX

Find all isolated singularities of the function
\[
f(z)=\sin(z)\sin\left(\frac{1}{z}\right)
\]
in \(\mathbb C\). Determine the residues of \(f\) at these isolated
singularities.

Topic Tags

Isolated Singularities and Residues