Padé Approximants 2nd Edition Hardback: 59 (Encyclopedia of Mathematics and its Applications, Series Number 59) - Tapa dura

Review of the hardback: 'There can only be one conclusion: this book is indispensable to the researcher and the would-be researcher in the field of Padé approximation ... one can only feel great admiration for the authors: they have done a splendid job incorporating all major developments in the theory and application of Padé approximation over the latest 15 years! Mathematika

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.