Pade Approximants: Encyclopedia of Mathematics and It's Applications, Vol. 59 George A. Baker, Jr., Peter Graves-Morris

Front Cover
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.
 

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Contents

1 Introduction and definitions
1
2 Elementary developments
38
3 Pade approximants and numerical methods
67
4 Connection with continued fractions
122
5 Stieltjes series and Pólya series
193
6 Convergence theory
276
7 Extensions of Padé approximants
335
8 Multiseries approximants
415
9 Connection with integral equations and quantum mechanics
570
10 Connection with numerical analysis
628
11 Connection with quantum Held theory
674
A FORTRAN FUNCTION
690
Bibliography
695
Index
741
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