Representation of theSMatrix by Regge Parameters

We express the $S$ matrix of complex angular momentum and positive energy by Regge poles, proving that a knowledge of the Regge poles enables one to determine the $S$ matrix uniquely. The background integral in the Mandelstam-Sommerfeld-Watson transform cannot be made to vanish by closing the contour to the left. Furthermore, one cannot express the scattering amplitude by an infinite-series sum of Regge-pole terms where each term is given by the Khuri representation.