On the computation of rational approximations to continuous functions

For each t, x(t) in Eq. ( It might be suspected that as N ~ the distribution of x(t) approaches a normal distribution with mean-zero and variance equal to R(0). Care must be exercised, however, since the A,~ coefficients are functions of N, as evidence by Eqs. (5). In other words, each case must be analyzed individually, as R(r) = cos r provides an example of a case in which the central limit theorem does not hold.