Pade Approximants

The Pade approximant of a given power series is a rational function of numerator degree L and denominator degree M whose power series agrees with the given one up to degree L + M inclusively. A collection of Pade approximants formed by using a suitable set of values of L and M often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, chemistry, electrical engineering, and other areas have led to a large number of generalizations of Pade approximants that are tailor-made for specific applications. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants. The book is written with a smooth progression from elementary ideas to some of the frontiers of research in approximation theory. Its main purpose is to make the various techniques described accessible to scientists, engineers, and other researchers who may wish to use them, while also presenting the rigorous mathematical theory.

This second edition is a comprehensive treatment of all straightforward aspects of Pade approximation, and the authors develop some themes to the level of current research. They extensively cover applications to statistical mechanics and critical phenomena, and there are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants. The new edition also contains a chapter on multiseries approximants. The book contains an extensive bibliography of recent monographs on other specialized material. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.