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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2008 • Question 7

Question

Math 6210 • Real Analysis Spring 2008 • Question 7

Show that the function \[ f(z)=\frac {\cos z}{z^2} \] is the complex derivative of a holomorphic function \(F\) on \(\mathbb C\setminus \{0\}\). Write down a Laurent series for \(F\).

Raw LaTeX

Show that the function
\[
f(z)=\frac{\cos z}{z^2}
\]
is the complex derivative of a holomorphic function \(F\) on
\(\mathbb C\setminus\{0\}\). Write down a Laurent series for \(F\).

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Laurent Series and Annuli Zeros of Holomorphic Functions and the Identity Theorem