I am a bit confused with the type of singularity at infinity for the following function.
$f(z) = z^2e^{(z-1/2)^2}\text{erfc}(z-1/2)$.
Alternatively, we can also use the Faddeeva function to re-write it as
$f(z) = z^2 w(i(z-1/2))$.
In the Wikipedia article, there is a statement on the presence of singularity at infinity for the error function. I suspect it is an essential singularity. If so, will the function $f(z)$ also contain an essential singularity at infinity, or will it be a pole of order 2?
Thank you in advance.