A ONE-PARAMETER FAMILY OF SEQUENCE TRANSFORMATIONS*

A one-parameter family of sequence or series transformations is presented which includes the Pade and the iterated Aitken’s (Shanks) tables as special cases. The transformation table elements are rational functions with polynomial coefficients in the parameter that, when expanded for small argument, are asymptotically equivalent to the highest order partial sum from which they are formed. Numerical examples using some standard series demonstrate dramatic acceleration of convergence and the ability to move branch cuts by choosing the parameter appropriately.