The proof of the Kutta-Joukowski theorem for the lift acting on a body (see: Wiki) assumes that the complex velocity $w'(z)$ can be represented as a Laurent series.
It is not surprising that the complex velocity can be represented by a Laurent series. But it surprises me that it is assumed that there are no positive powers of $z$ and it is also surprising that it is assumed that all the singularities are at $z=0$.
The Wikipedia article says it is deduced from the physics of the problem, which sounds pretty dubious to me. Another source says that this representation is valid for distances far away from the body, which is problematic as the square of the complex velocity is later integrated on the contour of the body.
Is there any way to explain that this form of the complex velocity is assumed?