On the use of Levin´s T-transform in accelerating the summation of series representing the free-space periodic Green´s functions

The Levin´s T-transform is shown to accelerate the summation of slowly converging series. This is illustrated by application of the transform to the series representing the free-space periodic Green´s functions involving a single and double infinite summation. Numerical results indicate that the transform converges more rapidly than a direct summation of the series. Thus, it provides considerable savings in computation time