Contents:Front Cover; The Padé Approximant in Theoretical Physics; Copyright Page; Contents; List of Contributors; Preface; Chapter 1. The Padé Approximant Method and Some Related Generalizations; I. Introduction; II. The Theory of the Padé Approximant Method; III. Generalized Approximation Procedures; IV. Applications; References; Chapter 2. Application of Padé Approximants to Dispersion Force and Optical Polarizability Computations; I. Introduction; II. Formalism; III. Computation Procedures; IV. Applications; V. Comparisions with Related Methods; VI. Concluding Remarks; References
Chapter 3. Bounds for Averages Using Moment ConstraintsI. Introduction; II. The Moments Problem; III. Applications; IV. Conclusion; Appendix A; Appendix B; References; Chapter 4. Turbulent Diffusion: Evaluation of Primitive and Renormalized Perturbation Series by Padé Approximants and by Expansion of Stieltjes Transforms into Contributions from Continuous Orthogonal Functions; I. Introduction; II. Continuous Orthogonal Expansion of Stieltjes Transforms; III. Examples Comparing Continuous Orthogonal Expansion and Padé Approximants; IV. Diffusion by a Random Velocity Field
V. Perturbation Expansions for the Diffusion ProblemVI. Approximants to the Primitive Perturbation Expansions; VII. Approximants to the Irreducible Expansion References; References; Chapter 5. Padé Approximants and Linear Integral Equations; I. Introduction; II. Properties of Linear Integral Equations; III. Integral Equations and Padé Approximants; IV. The Integral Equation for Potential Scattering References; References; Chapter 6. Series of Derivatives of d-Functions; I. Introduction; II. An Example; III. Expressions for g(k); IV. Approximants to g(k); V. Conclusions; References
Chapter 7. Hilbert Space and the Padé ApproximantI. Introduction; II. Extended Series of Stieltjes; III. Symmetric Operators and the Padé Approximant; IV. Method of Moments; V. Discussion; References; Chapter 8. The Connection of Padé Approximants with Stationary Variational Principles and the Convergence of Certain Padé Approximants; I. Introduction; II. Derivation of Padé Approximants from Stationary Variational Principles; III. Convergence of Padé Approximants; IV. The Convergence of Padé Approximants to Convergent Power Series; References
Chapter 9. Approximate N/D Solutions Using Padé ApproximantsI. Introduction; II. Method; III. Proof of Unitarity and Convergence; IV. Discussion; References; Chapter 10. The Solution of the N/D Equations Using the Padé Approximant Method; I. Introduction; II. The Integral Equations for Nand D and Their Approximate Solution; III. Convergent Sequences of Approximate Solutions to the N/D Equations; IV. The ? Bootstrap and Related Amplitudes; References; Chpater 11. Padé Approximants as a Computational Tool for Solving the Schrödinger and Bethe-Salpeter Equations; I. Introduction
II. Basic Philosophy and a Simple Example