Application of the Theory of Padé Approximants to the Solution of the N/D Equations

Abstract

Approximate methods for the solution of the N/D equations are discussed. Two methods in particular are considered, one being the replacement of the unphysical singularities of the scattering amplitude by a series of poles and the other being a pole approximation to the spectral integral of the kinematical factor over the physical region. It is shown that Padé approximants may be used to define a sequence of the above approximate solutions, which converges to the exact solution of the N/D equations in those cases when the Fredholm method also gives a solution.