Crossing Symmetric Expansions of Physical Scattering Amplitudes; The O(2, 1) Group and Lamé Functions

Abstract
An explicitly symmetric 2‐variable expansion, convergent in the physical regions of both the s and t channels, is obtained for 2‐body relativistic scattering amplitudes. Use is made of a symmetric mapping of the variables s and t onto a 2‐dimensional hyperboloid, leading to an expansion in terms of Lamé functions, which are the basis functions for an irreducible representation of the group O(2, 1) in our parametrization.