On the use of rho -algorithm in series acceleration

The rho -algorithm, a nonlinear transformation, is shown to be applicable to monotonic series. The results of applying the algorithm to a series involving the zeroth-order Hankel function of the second kind and its associated Fourier transform are given. It is shown that the algorithm performs better than the epsilon -algorithm derived from Shanks' transform (1955). Numerical results include a relative error measure versus number of terms taken in the series.<
>