  We give a general identity relating Eisenstein series on general linear
groups. We do it by constructing an Eisenstein series, attached to a maximal
parabolic subgroup and a pair of representations, one cuspidal and the other a
character, and express it in terms of a degenerate Eisenstein series. In the
local fields analogue, we prove the convergence in a half plane of the local
integrals, and their meromorphic continuation. In addition, we find that the
unramified calculation gives the Godement-Jacquet zeta function. This realizes
and generalizes the construction proposed by Ginzburg and Soudry in Section 3
in their aritcle "Integral derived from the doubling method".
