Limit at an Essential Singularity

Hello,

Given that z = w is an essential singulairty of a complex-valued function f(z),

I'm trying to determine that if z --> w, does it follow that f(z) neccecarily goes to infinity? (ie, lim (z-->w) f(z) = infinity)

I am trying to find a counterexample but cannot think of one, but also having trouble proving from the definition of essential singularity (in terms of Laurant series).

Any guidance helps! Thanks!

Re: Limit at an Essential Singularity

Re: Limit at an Essential Singularity

Quote:

Originally Posted by

**xxp9**

This is clearly an example of time travel since Jean Luc Picard will not actually prove the theorem until the 23rd century!