Applications of Conformal Mapping to the Phenomenological Representation of Scattering Amplitudes

A series representation of scattering amplitudes analytic in cut planes is derived by means of a conformal mapping. The new series has the advantage that in general it converges more rapidly than the conventional power series. An example is considered in which an angular distribution which requires ${\left(cos\theta \right)}^4$ terms for a good fit requires only second-order terms in the new series. The resulting advantages in using this series in extrapolations to poles are discussed. As a second example, a modified effective-range formula is derived.