In our lecture we defined the residue of a function $f(z)= \sum_{-\infty}^{\infty}a_nz^n$ as the coefficient $a_{-1}$ of the Laurent series.
We wanted to calculate the residue of $z\exp(\frac{1}{1-z})$.
In class they did it by substituting $z = 1+h$. So we get $(1+h)\exp(\frac{-1}{h}) = (1+h)(1-\frac{1}{h} + \frac{1}{2h^2} -...)$ The coefficient $a_{-1} = -1 + \frac{1}{2} = - \frac{1}{2}$
If I do the exact same calculation, but substitute $z = 1-h$, I get $a_{-1} = + \frac{1}{2}$.
Which of those solutions is correct? Is any of those solutions correct? I am a little bit confused right now.
Edit: I am dealing with the residude at $z=1$.