This paper presents a closed expansion of the convolution integral, which is useful in approximating the response of a linear time invariant system to an arbitrary forcing function. In a sense it is a generalization of the well known error coefficient expansion frequently discussed in connection with servomechanisms. This expansion is helpful when the response of the system cannot be evaluated exactly (i.e., the input function is specified graphically or input function cannot be transformed conveniently). This expansion differs from the error coefficient expansion in that it is valid for an arbitrary forcing function and is in a closed form accounting for the entire response of the system, rather than in an open form of Taylor's series that either neglects or simply bounds a portion of the total response.