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Exact finite series for the few‐body auxiliary functions
Author(s) -
Frolov Alexei M.,
Smith Vedene H.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:1<269::aid-qua28>3.0.co;2-5
Subject(s) - series (stratigraphy) , hypergeometric function , computation , series expansion , gaussian , simple (philosophy) , generalized hypergeometric function , function (biology) , mathematics , physics , mathematical analysis , quantum mechanics , algorithm , paleontology , philosophy , epistemology , evolutionary biology , biology
The so‐called few‐body auxiliary functions play a very important role in bound‐state calculations for nonrelativistic few‐body systems. In particular, the functions of the first, second, and third orders are used in four‐body calculations. By means of an original approach developed for the first time in the present study, we have found exact finite‐series representations for the auxiliary functions A n ( n ≤ 3). It is shown that the auxiliary functions A n are closely related to the Gaussian hypergeometric function 2 F 1 . A few simple 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. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 269–278, 1997