A functional expansion technique utilizing the Laplace-Borel transform is reviewed and applied to forced nonlinear processes with hyperbolic equilibrium points. Initial and final value theorems are presented to aid in the analysis of nonlinear systems. The expansions are shown to be equivalent to a linear transfer function with an added set of poles and zeros to capture the nonlinear dynamics of the system. The frequency response in the transform domain is derived as an analog to linear systems, with the resulting amplitude ratio and phase expressions being time dependent. The developed concepts are applied to a nonlinear CSTR example.