A general theory is developed of the expansions of a two particle scattering amplitude based on its Poincaré invariance properties for particles of arbitrary mass and spin. The theory is then applied to 1. (i) the conventional little group expansions, including the 0(3,1) expansion for equal mass, forward scattering 2. (ii) the auxiliary group expansions in terms of 0(3, 1) functions for the general case and 3. (iii) the double variable expansions of Smorodinsky et al. The implications of poles in these various amplitudes is discussed in connection with high energy behaviour and analyticity at zero momentum transfer. © 1969.
