Exercise · ZW-ISOLATED-SINGULARITY-001 · ★☆☆ Basic
What kind of singularity does \(\frac{\sin z}{z}\) have at \(z=0\)?
Choose one option.
Show answer
- A. Removable
Explanation
Since \(\frac{\sin z}{z}=1-\frac{z^2}{6}+\cdots\) has no negative powers and the limit at \(0\) is \(1\), the singularity is removed by defining \(f(0)=1\).
Review the concept: Isolated singularity
An isolated singularity of a function \(f\) is a point \(z_0\) where \(f\) is not holomorphic but is holomorphic on a punctured disc \(0<|z-z_0|<r\) around it.
More practice problems: isolated singularity
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