On the use of Shank's transform to accelerate the summation of slowly converging series

It is shown that the application of Shank's transform results in accelerating the convergence of slowly converging series. The transform is applied to a periodic Green's function involving a single summation. The convergence properties of this series are reported for the on-plane case, in which the series converges extremely slowly. Numerical results indicate that by using Shanks' transform the computation time can be reduced by as much as a factor of 200.>