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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2010 • Question 7

Question

Math 6210 • Real Analysis Fall 2010 • Question 7

Let \[ f(z)=\sin \left (\frac {z}{z+1}\right ). \] (i) Determine all isolated singularities of \(f\) and their type;

(ii) Find the Laurent expansions of \(f\) at these singularities;

(iii) Find the residues of \(f\) at these singularities.

Raw LaTeX

Let
\[
f(z)=\sin\left(\frac{z}{z+1}\right).
\]
(i) Determine all isolated singularities of \(f\) and their type;

(ii) Find the Laurent expansions of \(f\) at these singularities;

(iii) Find the residues of \(f\) at these singularities.

Topic Tags

Isolated Singularities and Residues Laurent Series and Annuli