# Nature of singularity

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1. Aug 6, 2015

### ion santra

what is the nature of singularity of the function f(x)=exp(-1/z) where z is a complex number?
now i arrive at two different results by progressing in two different ways.
1) if we expand the series f(z)=1-1/z+1/2!(z^2)-... then i can say that z=0 is an essential singularity.
2) now again if i take the limit of the function from either sides of zero, i see it exists finitely, therefore not a singular point at all.

2. Aug 6, 2015

### micromass

It is an essential singularity.

Can you expand on this? Don't forget that $z$ is a complex number, so just taking the two sided limits in $\mathbb{R}$ is not good enough.

3. Aug 6, 2015

### mathman

For Real z < 0, the limit as z ->0 is infinite.