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 consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall 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 whet the appetite is presented first, before the more basic but modernized theory is given.

This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.


  • Introductory Examples
  • Basics
  • Convergence Criteria
  • Periodic and Limit Periodic Continued Fractions
  • Numerical Computation of Continued Fractions
  • Some Continued Fraction Expansions

Readership: Academics, researchers and graduate students in continued fractions.  

“The authors are leaders in the field, and have a long and productive history working with continued fractions. Indeed, many modern advances in analytic theory of continued fractions can be attributed to their work. The authors are therefore able to bring a deep and rich background to the subject … The book is nicely written and a pleasure to read. The subject matter is well developed, rigorous, and extensive … This book should be of great value both as a reference book and as a classroom textbook suitable for advanced undergraduates, graduate students, and interested researchers. Beginning students at the senior/graduate level should find this an invaluable resource for their studies, while researchers will find perspectives and results conveniently organized and presented for reference.” Phil Gustafson, Professor of Mathematics Mesa State College, Colorado
“This book is clearly written and well presented. It also contains many examples to illustrate the results … for expert or a researcher, it is a gold mine! Readers who already know its first edition will certainly find this volume more interesting.” Phil Gustafson, Professor of Mathematics Mesa State College, Colorado.

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: March 2008
Hardbound, 308 pages
Price: €80.00


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