9780486823690

One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful.
The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.

Hubert Stanley Wall (1902–71) received his Ph.D. from the University of Wisconsin. He taught at Northwestern and the Illinois Institute of Technology before joining the faculty of the University of Texas at Austin in 1946, where he spent the rest of his career and supervised more than 60 mathematics doctoral students.

Contents:
Preface
Introduction
Chapter I: The Continued Fraction as a Product of Linear Fractional Transformations.
Chapter II: Convergence Theorems.
Chapter III: Convergence of Continued Fractions Whose Partial Denominators are Equal to Unity.
Chapter IV: Introduction to the Theory of Positive Definite Continued Fractions.
Chapter V: Some General Convergence Theorems.
Chapter VI: Stieltjes Type Continued Fractions.
Chapter VII: Extensions of the Parabola Theorem.
Chapter VIII: The Value Region Theorem.
Chapter IX: J-Fraction Expansions for Rational Functions.
Chapter X: Theory of Equations.
Chapter XI: J-Fraction Expansions for Power Series.
Chapter XII: Matrix Theory of Continued Fractions.
Chapter XIII: Continued Fractions and Definite Integrals.
Chapter XIV: The Moment Problem For a Finite Interval.
Chapter XV: Bounded Analytic Functions.
Chapter XVI: Hausdorff Summability.
Chapter XVII: The Moment Problem For an Infinite Interval.
Chapter XVIII: The Continued Fraction of Gauss.
Chapter XIX: The Stieltjes Summability.
Chapter XX: The Pade Table. (e in Pade needs acute accent)
Bibliography.
Index.

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Analytic Theory of Continued Fractions

Analytic Theory of Continued Fractions

0486823695

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