We derive a series expansion for i//(z) in which the terms of the expansion are simple rational functions of z. From a computational viewpoint, the new series is of interest in that it converges for all z not necessarily real valued, and is particularly rapid for values of z near the origin. From a mathematical viewpoint the series is of interest in that, although \fr(z) has poles at the negative integers and zero, the series is uniformly convergent in any finite interval a < Re(z) < b.