Continued Fractions
(2nd Edition)
Volume 1: Convergence Theory
ISBN: 978-90-78677-07-9
Lisa Lorentzen and Haakon Waadeland
Norwegian University of Science and Technology, Trondheim, Norway
Series: Atlantis Studies in Mathematics for Engineering and Science, Volume 1.
Continued Fractions will consist of 2 Volumes: Volume 1: Convergence Theory and Volume 2: Representation of functions (tentative title). The two volumes will present the basic continued fraction theory without requiring too much previous knowledge. (Some basic knowledge of complex functions suffices.) Graduate students and old and new users of continued fractions will get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to wet the appetite is presented before continuing with the more basic, but modernized theory. The increasing interest in computing special functions by means of continued fractions has been one of the many reasons for writing this new edition. The methods are in many important cases simple, reliable and very efficient. They are described in detail and it is explained how they work, and why they work so well.
In 1992 “Continued Fractions with Applications” was published by Elsevier in the series “Studies in Computational Mathematics”. These two volumes are a follow-up and extension of this book. Although there have been some other books on continued fractions on the market since then, these are aimed at more special applications, and not at the basic theory. There are two particular reasons why it is important that volume 1 and volume 2 appear in print. The first one is the natural development of the field over the past 15 years since 1992. The second reason is the fact that Springer will publish the Handbook of Continued Fractions for Special Functions, by Cuyt, A., Petersen, V.B., Verdonk, B., Waadeland, H., Jones, W.B., a handbook on computing special functions by means of continued fractions. The methods proposed in this handbook are based on works by Haakon Waadeland and Lisa Lorentzen, among others, and they are well described in these two volumes. We expect an increase of interest in these methods once the handbook of Continued Fractions for Special Functions has appeared.
Features & Benefits
- New and updated information;
- A more elementary introduction to the field and a wealth of problems which can be found at the end of each chapter;
- The use of tail sequences, general convergence and restrained sequences in order to simplify some proofs in the theory. They also give a better understanding of what happens when a continued fraction converges or diverges;
- Some of the results in the book are new and not published elsewhere.
Table of contents
Preface to the 2nd Edition
Preface to the 1st Edtion
1. Introductory examples
2. Basics
3. Convergence criteria
4. Periodic and limit periodic continued fractions
5. Numerical computation of continued fractions
A. Some continued fraction expansions
References
Index
Audience
Mathematicians, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduates who would like an extensive introduction to the analytic theory of continued fractions, researchers.
Publishing Date: May 2008
Hardbound, v – xii + 308 pages
Price: €80.00.