Newtonian, Post Newtonian and Parameterized 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 and Parameterized Post Newtonian 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.