High precision evaluation of the irregular Coulomb wave functions

Abstract

This tutorial paper presents practical methods for accurately evaluating irregular Coulomb wave functions. Rational approximations to G 0 ( η , ρ ) {G_0}(\eta ,\rho ) and G 0 ′ ( η , ρ ) {G’_0}(\eta ,\rho ) are developed along line segments in the ( η , ρ ) (\eta ,\rho ) plane to provide useful initial values for the associated differential equation. These approximations, designed for IBM System 360 Fortran double precision, yield results to at least 13 significant decimal places.