Asymptotic Expansion of Irregular Coulomb Function for Angular Momentum Zero

A justification is given for an expansion of the irregular Coulomb function, usually denoted by G₀, in terms of Bessel functions of the second kind with an imaginary argument. This expansion has been considered speculatively by Yost, Wheeler, and Breit and explicitly verified by Breit and Bouricius for a number of terms. A general rule of replacement of the Bessel functions of the first kind with an imaginary argument in the corresponding expansion of the regular Coulomb function is here established. The formulas developed are convenient for the calculation of coefficients of the energy.