Diffraction of a plane wave at a perfectly conducting moving edge

We analyse the diffraction of an harmonic plane wave incident normally on the edge of a perfectly conducting half-plane moving with a constant velocity in a direction perpendicular to the screen. In the co-moving frame where the screen is at rest, we have to deal with the old Poincare-Sommerfeld diffraction problem that we solve with a technique borrowed from Bateman because this technique makes it easy the use of Lorentz transformations to get the solution in the laboratory frame. Some possible generalizations are discussed.