An expansion is derived for the regular (power series) part of the Coulomb function, G0(η, ρ), in terms of Whittaker functions, which are closely related to the regular Coulomb functions F1 (η, ρ). 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 G1(η, ρ), in particular for an attractive potential (η < 0) and for small or moderately large values of ρ.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications