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CONTINUED FRACTIONS

  • Book
  • © 2008

Overview

Authors:
  1. Lisa Lorentzen

    1. Department of Mathematics, Norwegian University of Science and Technology, Trondheim, Norway

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  2. Haakon Waadeland

    1. Department of Mathematics, Norwegian University of Science and Technology, Trondheim, Norway

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Atlantis Studies in Mathematics for Engineering and Science (ASMES, volume 1)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introductory examples

    • Lisa Lorentzen, Haakon Waadeland
    Pages 1-52

  3. Basics

    • Lisa Lorentzen, Haakon Waadeland
    Pages 53-98

  4. Convergence criteria

    • Lisa Lorentzen, Haakon Waadeland
    Pages 99-170

  5. Periodic and limit periodic continued fractions

    • Lisa Lorentzen, Haakon Waadeland
    Pages 171-216

  6. Numerical computation of continued fractions

    • Lisa Lorentzen, Haakon Waadeland
    Pages 217-264

  7. Back Matter

    Pages 265-308
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Norwegian University of Science and Technology, Trondheim, Norway

    Lisa Lorentzen, Haakon Waadeland

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