In the investigation of two-body Coulomb Schrödinger equations with some types of nonhomogeneities, the particular solution can be expressed in terms of a two-variable Kampé de Fériet hypergeometric function. The asymptotic limit of the latter—for both variables being large but their ratio being a bound constant—is required in order to extract relevant physical information from the solutions. In this report the mathematical limit is provided. For that purpose, a particular series representation of the hypergeometric function—in terms of products of Kummer and Gauss functions—is first derived.
REFERENCES
1.
A. W.
Babister
, Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations
(The Mcmillan Company
, New York
, 1967
).2.
R. G.
Newton
, Scattering Theory of Waves and Particles
(Dover Publications INC
, New York
, 2002
).3.
C. J.
Joachain
, Quantum Collision Theory
(Noth-Holland Publishing Company
, Amsterdam
, 1983
).4.
G.
Gasaneo
and L. U.
Ancarani
, Phys. Rev. A
82
, 042706
(2010
).5.
P.
Appell
and J. Kampé de
Fériet
, Fonctions Hypergéométriques et Hypersphériques; Polynomes d’Hermite
(Gauthier-Villars
, Paris
, 1926
).6.
L. U.
Ancarani
and G.
Gasaneo
, J. Math. Phys.
49
, 063508
(2008
).7.
M.
Abramowitz
and I. A.
Stegun
, Handbook of Mathematical Functions
(Dover
, New York
, 1972
).8.
A.
Erdelyi
, W.
Magnus
, F.
Oberhettinger
, and F. G.
Tricomi
, in Higher Trascendental Functions
(McGraw-Hill
, New York
, 1953
), Vol. I–III
.© 2011 American Institute of Physics.
2011
American Institute of Physics
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