Singular behavior of the multipole electromagnetic field

The singularities of the electromagnetic field are derived to include all the pointlike multipoles representing an electric charge and current distribution. In the static case, the δ-singularities are expressed for arbitrary multipole orders, while in the dynamic case we restrict ourselves to the lower orders. The algorithm we give can be easily extended to the next orders. In both cases, we show that for higher orders, it is more efficient to have fields represented in terms of symmetric and trace-free moments.