On the use of Chebyschev-Toeplitz algorithm in accelerating the numerical convergence of infinite series

It is shown that a simple application of the Chebyschev-Toeplitz algorithm enhances the rate of convergence of slowly converging series. The algorithm is applied to series representing the periodic Green´s functions involving a single infinite summation. The algorithm yields highly accurate results within relatively fewer terms. A quantitative comparison is shown with methods previously reported in the literature