Show that if ƒ has an essential singularity at zo, then either has an essential singularity at zo or has a sequence of poles converging to zo (making zo a nonisolated singularity).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Essential Singularity and Poles**

*Show that if \( f \) has an essential singularity at \( z_0 \), then either \( \frac{1}{f} \) has an essential singularity at \( z_0 \) or \( \frac{1}{f} \) has a sequence of poles converging to \( z_0 \) (making \( z_0 \) a nonisolated singularity).*
Transcribed Image Text:**Essential Singularity and Poles** *Show that if \( f \) has an essential singularity at \( z_0 \), then either \( \frac{1}{f} \) has an essential singularity at \( z_0 \) or \( \frac{1}{f} \) has a sequence of poles converging to \( z_0 \) (making \( z_0 \) a nonisolated singularity).*
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