Representations of the S Matrix in Terms of Its Angular Momentum Poles

The asymptotic distribution of poles of the nonrelativistic S matrix for potential scattering in the complex angular momentum plane is investigated, and so is the nature of the pole trajectories near $E=0$. As a consequence of the behavior of the distant poles and of their residues the S matrix is shown to be representable in the form of an infinite (Weierstrass-Hadamard) product as well as in the form of a (Mittag-Leffler) series of partial fractions.