EXACT FINITE SERIES FOR THE FEW-BODY AUXILIARY FUNCTIONS

The so-called few-body auxiliary functions play a very important role in bound-state calculations for nonrelativistic few-body systems. In p articular, the functions of the first, second, and third orders are us ed in four-body calculations. By means of an original approach develop ed for the first time in the present study, we have found exact finite -series representations for the auxiliary functions A(n) (n less than or equal to 3). It is shown that the auxiliary functions A(n) are clos ely related to the Gaussian hypergeometric function F-2(1). A few simp le finite-series.expansions are also presented, which seem to be very convenient for numerical computations. This work opens a new avenue in the study of auxiliary functions and their properties. (C) 1997 John Wiley & Sons, Inc.