The new recently introduced [J. Chem. Phys 102, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [E-(($) over cap H+Gamma)](-1), Gamma being a simple complex optical potential. The expansion is energy separable and converges uniformly in the real energy domain. The scaling of the Hamiltonian is trivial and does not involve complex analysis. Formal use of the energy-to-time Fourier transform of the ABC (absorbing boundary conditions) Green’s function leads to a recursion polynomial expansion of the ABC time evolution operator that is global in time. Results at any energy and any time can be accumulated simultaneously from a single iterative procedure; no actual Fourier transform is needed since the expansion coefficients are known analytically. The approach can be also used to obtain a perturbation series for the Green’s function. The new iterative methods should be of a great use in the area of the reactive scattering calculations and other related fields.