Floquet close-coupling (FCC) analysis of stimulated electron - hydrogen scattering in the field of a low-frequency laser field is carried out. Results are obtained for one-, two- and three-photon absorption and emission processes in terms of the differential scattering cross sections as a function of the scattering angle. Two critical geometries are considered in which the argument of the Bessel function in the well known low-frequency formula becomes negligibly small. It is found that the ratios of the cross sections for small-angle scattering in both geometries are many orders of magnitude larger than predicted by the low-frequency formula (LFF). The result supports an analogous finding of many orders of magnitude larger values of the cross section measured in Ar and He by Wallbank and Holmes, and confirms the failure of LFF for small-angle scattering.