The Padé Approximation and its Physical Applications

The Padé approximation, its mathematical features, and its practical and physical applications are reviewed. We describe the present status of the convergence problem. Among the physical applications, we give particular emphasis to elementary particle theory. We discuss various proofs of convergence, and show why the approximation is particularly well suited for studying strong interaction dynamics. We finally review the various achievements of the approximation in the determination of ππ, πN and NN scattering amplitudes.