# Integrals of the function f(z) = e^(1/z) (complex analysis)

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1. Apr 16, 2015

### Matt100

How do you integrate f(z) = e^(1/z) in the multiply connected domain {Rez>0}∖{2}

It seems like integrals of this function are path independent in this domain since integrals of e^(1/z) exist everywhere in teh domain {Rez>0}∖{2}. Is that correct?

Last edited: Apr 16, 2015
2. Apr 16, 2015

### Staff: Mentor

I agree.
Where is the point in excluding that point, by the way? It is not special.

3. Apr 17, 2015

### Svein

I seem to remember that the function given by f(z)=0 for Re(z)≤0 and $f(z)=e^{-\frac{1}{z}}$ for Re(z)>0 is ℂ in the whole complex plane, but not analytic...

4. Apr 17, 2015

### Staff: Mentor

Why?
The Laurent series is easy to construct here.

5. Apr 18, 2015

### Svein

Sorry, that should be C.