In potential scattering theory we consider the question of the angular-momentum continuation of the radial wave function. We assume that at a fixed value ofl (s-wave) we can solve the radial wave equation for both the regular solution (wave function) and the irregular solution. From this knowledge we construct an integral equation for the wave function which allows it to be analytically continued in angular momentum. Although the kernel of this integral equation is singular, the iterative solution is shown to exist in a limited region. An analysis of the spectrum of this kernel yields an interesting integral identity for the irregular solution of the wave equation. On the basis of this analysis we conjecture an integral representation of the wave function (regular solution) in terms of the irregular solution. For a limited class of potentials this representation is shown to hold in perturbation theory and to afford a view of all singularities in the left-halfl-plane.