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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 7

Question

Math 6210 • Real Analysis 2005 • Question 7

Let \[ f(z)=\frac {e^{\frac {1}{z-1}}}{e^z-1}. \] Determine all isolated singularities of \(f\) and their type. Find the residues of \(f\) at its poles.

Raw LaTeX

Let
\[
f(z)=\frac{e^{\frac{1}{z-1}}}{e^z-1}.
\]
Determine all isolated singularities of \(f\) and their type. Find the residues of
\(f\) at its poles.

Topic Tags

Isolated Singularities and Residues