This paper investigates the connection between the homogeneous and inhomogeneous equations for the Coulomb scattering wave function of two particles. It is shown that the form of the equation depends on the method used to regularize the divergent integrals in the homogeneous part of the equation. This result is a generalization of the result obtained by Van Haeringen for orbital angular momentum equal to zero. It is also shown to be helpful to introduce a Coulomb asymptotic state in the momentum representation; this is the inhomogeneous part of the equation and contains all the principal information about the forward scattering of charged particles. The Coulomb asymptotic states can be used to find the behavior of the reaction amplitudes of charged particles near singularities in cos 0, where 0 is the scattering angle.