Book contents
- Frontmatter
- Contents
- Editor's Statement
- Section Editor's Foreword
- Introduction by Peter Henrici
- Preface
- Symbols
- Continued Fractions
- Chapter 1 Introduction
- Chapter 2 Elementary Properties of Continued Fractions
- Chapter 3 Periodic Continued Fractions
- Chapter 4 Convergence of Continued Fractions
- Chapter 5 Methods for Representing Analytic Functions by Continued Fractions
- Chapter 6 Representations of Analytic Functions by Continued Fractions
- Chapter 7 Types of Corresponding Continued Fractions and Related Algorithms
- Chapter 8 Truncation-Error Analysis
- Chapter 9 Asymptotic Expansions and Moment Problems
- Chapter 10 Numerical Stability in Evaluating Continued Fractions
- Chapter 11 Application of Continued Fractions to Birth-Death Processes
- Chapter 12 Miscellaneous Results
- Appendix A Classification of Special Types of Continued Fractions
- Appendix B Additional Results on Minimal Solutions of Three-Term Recurrence Relations
- Bibliography
- Author Index
- Subject Index
Editor's Statement
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Editor's Statement
- Section Editor's Foreword
- Introduction by Peter Henrici
- Preface
- Symbols
- Continued Fractions
- Chapter 1 Introduction
- Chapter 2 Elementary Properties of Continued Fractions
- Chapter 3 Periodic Continued Fractions
- Chapter 4 Convergence of Continued Fractions
- Chapter 5 Methods for Representing Analytic Functions by Continued Fractions
- Chapter 6 Representations of Analytic Functions by Continued Fractions
- Chapter 7 Types of Corresponding Continued Fractions and Related Algorithms
- Chapter 8 Truncation-Error Analysis
- Chapter 9 Asymptotic Expansions and Moment Problems
- Chapter 10 Numerical Stability in Evaluating Continued Fractions
- Chapter 11 Application of Continued Fractions to Birth-Death Processes
- Chapter 12 Miscellaneous Results
- Appendix A Classification of Special Types of Continued Fractions
- Appendix B Additional Results on Minimal Solutions of Three-Term Recurrence Relations
- Bibliography
- Author Index
- Subject Index
Summary
A large body of mathematics consists of facts that can be presented and described much like any other natural phenomenon. These facts, at times explicitly brought out as theorems, at other times concealed within a proof, make up most of the applications of mathematics, and are the most likely to survive changes of style and of interest.
This ENCYCLOPEDIA will attempt to present the factual body of all mathematics. Clarity of exposition, accessibility to the non-specialist, and a thorough bibliography are required of each author. Volumes will appear in no particular order, but will be organized into sections, each one comprising a recognizable branch of present-day mathematics. Numbers of volumes and sections will be reconsidered as times and needs change.
It is hoped that this enterprise will make mathematics more widely used where it is needed, and more accessible in fields in which it can be applied but where it has not yet penetrated because of insufficient information.
- Type
- Chapter
- Information
- Continued FractionsAnalytic Theory and Applications, pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 1984