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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2013 • Question 8

Question

Math 6210 • Real Analysis Spring 2013 • Question 8

Find the Laurent series of the function \[ f(z)=\frac {1}{(z-z^2)^2} \] at \(z=0\).

(a) What kind of isolated singularity does \(f\) have at \(0\)?

(b) What is the residue of \(f\) at \(0\)?

Raw LaTeX

Find the Laurent series of the function
\[
f(z)=\frac{1}{(z-z^2)^2}
\]
at \(z=0\).

(a) What kind of isolated singularity does \(f\) have at \(0\)?

(b) What is the residue of \(f\) at \(0\)?

Topic Tags

Isolated Singularities and Residues Laurent Series and Annuli