Newtonian, Post-Newtonian and Parametrized Post-Newtonian limits of f(R, G) gravity

We discuss in detail the weak field limit of f(R, G) gravity taking into account analytic functions of the Ricci scalar R and the Gauss-Bonnet invariant G. Specifically, we develop, in metric formalism, the Newtonian, Post-Newtonian (PN) and Parametrized Post-Newtonian (PPN) limits starting from general f(R, G) Lagrangian. The special cases of f(R) and f(G) gravities are considered. In the case of the Newtonian limit of f(R, G) gravity, a general solution in terms of Green's functions is achieved.