To overcome this limitation, we introduce a hierarchical summation scheme reminiscent of the treecode algorithm used in FMM. The key insight is to recognize that the distance appears in the complex exponential argument of eqn. ( ) as a product of the form αr 12 , which permits a given set of quadrature parameters to describe greater r 12 distances if there is a concomitant reduction in the value of α; the different values of α used will be referred to as the "scale" of the interaction in the following discussion. To utilize this property, we need a scheme to allow scaling of α without affecting the results, which we will now describe using a simple example.