Padé Approximants (Encyclopedia of Mathematics and its Applications, Series Number 59)

The First Edition Of This Book Was Reviewed In 1982 As 'the Most Extensive Treatment Of Padé Approximants Actually Available'. This Second Edition Has Been Thoroughly Updated, With A Substantial Chapter On Multiseries Approximants. Applications To Statistical Mechanics And Critical Phenomena Are Extensively Covered, And There Are Extended Sections Devoted To Circuit Design, Matrix Pade Approximation, And Computational Methods. This Succinct And Straightforward Treatment Will Appeal To Scientists, Engineers, And Mathematicians Alike. George A. Baker, Jr., Peter Graves-morris. Includes Bibliographical References And Index. 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. Now in paperback, this is a graduate level text for theoretical physicists and mathematicians which systematically lays out the foundations for the subject of Quantum Groups in a clear and accessible way. The topic is developed in a logical manner with quantum groups (Hopf Algebras) treated as mathematical objects in their own right. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. Explicit proofs and many examples will allow the reader quickly to pick up the techniques needed for working in this exciting new field This second edition is a comprehensive treatment of all straightforward aspects of Pad 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 Pad 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. Thoroughly updated, with material on multiseries approximants, circuit design, matrix Padé approximation and computational methods.