AMS Chelsea Publishing 1948; 433 pp; hardcover Volume: 207 Reprint/Revision History: reprinted 1973; first AMS printing 2000 ISBN10: 0821821067 ISBN13: 9780821821060 List Price: US$57 Member Price: US$51.30 Order Code: CHEL/207.H
 The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is on the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extended discussions of orthogonal polynomials, power series, infinite matrices and quadratic forms in infinitely many variables, definite integrals, the moment problem and the summation of divergent series. "In writing this book, I have tried to keep in mind the student of rather modest mathematical preparation, presupposing only a first course in function theory. Thus, I have included such things as a proof of Schwarz's inequality, theorems on uniformly bounded families of analytic functions, properties of Stieltjes integrals, and an introduction to the matrix calculus. I have presupposed a knowledge of the elementary properties of linear fractional transformations in the complex plane. "It has not been my intention to write a complete treatise on the subject of continued fractions, covering all the literature, but rather to present a unified theory correlating certain parts and applications of the subject within a larger analytic structure ... " from the Preface Readership Graduate students and research mathematicians. Table of Contents Part I: Convergence Theory  The continued fraction as a product of linear fractional transformations
 Convergence theorems
 Convergence of continued fractions whose partial denominators are equal to unity
 Introduction to the theory of positive definite continued fractions
 Some general convergence theorems
 Stieltjes type continued fractions
 Extensions of the parabola theorem
 The value region problem
Part II: Function Theory  Jfraction expansions for rational functions
 Theory of equations
 Jfraction expansions for power series
 Matrix theory of continued fractions
 Continued fractions and definite integrals
 The moment problem for a finite interval
 Bounded analytic functions
 Hausdorff summability
 The moment problem for an infinite interval
 The continued fraction of Gauss
 Stieltjes summability
 The Padé table
 Bibliography
 Index
