The S matrix associated with a central potential is shown to be meromorphic in the energy and angular momentum variables under very broad conditions. The domain of meromorphy contains the product of a domain in the energy variable by a domain in the angular variable. The former (latter) domain has a very simple connection with the domain of meromorphy of the Laplace (Mellin) transform of the potential with respect to the radius.
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M. Froissart (1962) studied this question.