We consider three-dimensional acoustical scattering or radiation problems in frequency domain above an infinite flat plane equipped with a local impedance condition. For such half-space problems, a BEM formulation is of advantage, where the Green’s function used satisfies not only the Helmholtz equation, but also the boundary condition at the impedance plane. When using such a tailored Green’s function, only the surface of the sound radiating or scattering object has to be discretized, since the influence of the impedance ground is automatically taken into account. Simple formulas for such half-space Green’s function exist only for rigid or soft infinite planes. For a ground with arbitrary surface impedances, many different expressions of the Green’s function are given in the literature. For incorporating these functions into a BEM formulation, the first and second normal derivatives must be calculated in such a way that they do not possess strong singularities. In the present work, four representations o...