HSC would like to thank (1) the Department of Physics & Astronomy at Louisiana
State University (LSU) as well as (2) LSU Prof. Juhan Frank for providing travel
and accomodations support for attendance at the 200th IAU symposium on
binary star formation in Potsdam, Germany and (3) LSU Prof. Dana A. Browne for his
support during the course of this work. ARPR thanks the Alexander von Humboldt
Stiftung and Profs. J. Hinze and F. H. M. Faisal of the University of Bielefeld for
their hospitality during the course of this work. Thanks to E. G. Kalnins for many
inspiring communications and for providing the Moon & Spencer (1961b) reference.
Thanks to J. D. Jackson for pointing out the Magnus, Oberhettinger & Soni (1966)
reference which gives a further generalization of the Heine identity. Thanks are
also due to J. E. Lambert for several subtle grammatical criticisms and suggestions.
We acknowledge support from NASA through grant NAG5-8497 and from the NSF through
grant AST-9987344. This work also has been supported, in part, by a grant of
high-performance computing time on NPACI facilities at the SDSC.
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Presently there are many applications for determining the Newtonian/Coulomb
potentials in theoretical physics. In astrophysics, the need for accurate
methods to calculate gravitational fields is ubiquitous. Similarly, physicists
require the Coulomb fields in many different types of problems. We have
intent to pursue in depth in the future Lie group theoretical implications
of these results (Miller 1968, 1972, 1977).
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