Ornstein-Zernike equation with core condition and direct correlation function of Yukawa form

A detailed explication of the analytic structure of the Ornstein-Zernike equation with a core condition and a direct correlation function of Yukawa form is given. The solution found by Waisman [4] is simplified. The resulting analytic expressions are the basis of the generalized mean spherical results of Stell and Sun [7] for charged spheres and are fundamental to the approximation scheme of Høye and Stell [8] for polar fluids. Our study of the case of a two-Yukawa c(r) [following article] is also based upon the development given here.