The Pade approximation and its physical applications

The Pade approximation, its mathematical features, and its practical and physical applications are reviewed. The author describes the present status of the convergence problem. Among the physical applications, he gives particular emphasis to elementary particle theory. He discusses various proofs of convergence, and show why the approximation is particularly well suited for studying strong interaction dynamics. He finally reviews the various achievements of the approximation in the determination of pi pi , pi N and NN scattering amplitudes. (100 refs).