Neumann-type expansion of Coulomb functions (Q1326708)

The paper gives an expansion of the irregular Coulomb function \(G_ 0(\eta,\rho)\) in terms of the regular Coulomb functions \(F_ L(\eta,\rho)\). The series can be viewed as the analogue of the Neumann series for the Bessel functions, in which the Bessel function \(Y_ 0(z)\) is expressed as a series of Bessel functions \(J_ n(z)\). The authors discuss the use of the Neumann-type expansion of the Coulomb functions for computing the irregular Coulomb function. The authors (and the journal editor(s) and referee(s)) seem to be unaware of a more advanced paper that gives similar, more and better results. It concerns the paper of \textit{J. Boersma} [Math. Comput. 23, 51-59 (1969; Zbl 0181.334)]. The coefficients in Boersma's Neumann-type series are given in terms of simple explicit expressions, whereas in the present paper the coefficients are to be computed by using three-term recurrence relations.