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Neumann-Type Expansion of Coulomb Functions

โœ Scribed by P. Marksteiner; E. Badralexe; A.J. Freeman

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
156 KB
Volume
111
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

An expansion is derived for the regular (power series) part of the Coulomb function, (G_{0}(\eta, \rho)), in terms of Whittaker functions, which are closely related to the regular Coulomb functions (F_{1}(n, \rho)). The expansion coefficients are given as a sum of three terms; each of the terms obeys a simple three-term recurrence relation. In conjunction with the downward recurrence method for the regular functions (which is also discussed), this expansion is very useful for computing the irregular Coulomb functions (G_{1}(n, \rho)), in particular for an attractive potential ((n<0)) and for small or moderately large values of (\rho) (1994 Academic Press, inc.

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