For the description of an arbitrary nonrelativistic three-body Coulomb system an analytical approximate wave function is designed which is correct for large interparticle separations. At shorter distances, where the potential energy dominates the kinetic one, the wave function is a linear mixture of products each consisting of three two-body Coulomb waves propagating off the two-body energy shell but on the total energy shell. The method is employed for the calculations of multiply differential cross sections for photo-double ionization of helium and for electron, positron, proton, and antiproton-impact ionization of atomic hydrogen.