The Hormander solution singular at a running point and the Bateman solution

In order to illustrate his theory of propagation of wavefront sets for hyperbolic equations, Hörmander gave in [1] the first example of a solution of the wave equation, that has a singularity at a single point running with time. We analyze the analytical structure of this solution for the case of the wave equation with three spatial variables. Our most remarkable observation is that it reduces to the classical, non-complexified Bateman solution [2,3].