Fourier coefficients of Eisenstein series for $O^{+}(2,n+2)$

We derive the Fourier expansion of scalar-valued Eisenstein series for O(2, n+2) using classical methods of Siegel, Braun, Zagier, Bruinier and others. We assume that the underlying lattice splits two hyperbolic planes. Finally we prove for the Eisenstein series at the standard cusp that they belong to the Maass space for O(2, n + 2), an analogue of the “Spezialschar” for Siegel modular forms introduced by Maass, at least at all local places p, where the localization of the underlying lattice is maximal.