Convergent and asymptotic series in the energy are derived for an irregular Coulomb function appropriate to both attractive and repulsive potentials. The coefficients in these series are Bessel functions. For repulsive potentials the derivation yields series in agreement with those given by Breit and others. Some of the series for attractive potentials have been given by Kuhn. The present general derivation and some of the series are, however, new. Tables of the coefficients in the series for the attractive potentials for values of the parameters of interest in solid state energy band calculations have been prepared and are available.