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Continued Fractions

Convergence Theory

  • Lisa Lorentzen
  • Haakon Waadeland
Book

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Lisa Lorentzen, Haakon Waadeland
    Pages 1-52
  3. Lisa Lorentzen, Haakon Waadeland
    Pages 53-98
  4. Lisa Lorentzen, Haakon Waadeland
    Pages 99-170
  5. Lisa Lorentzen, Haakon Waadeland
    Pages 171-216
  6. Lisa Lorentzen, Haakon Waadeland
    Pages 217-264
  7. Back Matter
    Pages 265-308

About this book

Introduction

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.

Keywords

Finite Meromorphic function Volume computation computation of continued fractions continued fraction convergence function functions knowledge presentation special function

Authors and affiliations

  • Lisa Lorentzen
    • 1
  • Haakon Waadeland
    • 1
  1. 1.Department of MathematicsNorwegian University of Science and TechnologyTrondheimNorway

Bibliographic information