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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 9

Question

Math 6210 • Real Analysis 2005 • Question 9

Let \(f\) be a holomorphic function with isolated singularity at point \(a\). Assume that \(g=\frac {1}{f}\) also has an isolated singularity at \(a\), and that \(a\) is not a removable singularity for either \(f\) or \(g\). Determine what type of isolated singularity \(a\) is for \(f\) and \(g\).

Do you know an example of such a function \(f\)?

Raw LaTeX

Let \(f\) be a holomorphic function with isolated singularity at point
\(a\). Assume that \(g=\frac{1}{f}\) also has an isolated singularity at \(a\), and
that \(a\) is not a removable singularity for either \(f\) or \(g\). Determine what
type of isolated singularity \(a\) is for \(f\) and \(g\).

Do you know an example of such a function \(f\)?

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Isolated Singularities and Residues Zeros of Holomorphic Functions and the Identity Theorem