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History of Continued Fractions and Padé Approximants

  • Book
  • © 1991

Overview

Authors:
  1. Claude Brezinski

    1. Laboratoire d’Analyse Numérique et d’Optimisation UFR IEEA-M3, Université des Sciences et Techniques, Villeneuve d’Ascq Cedex, France

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Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 12)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Claude Brezinski
    Pages 1-2

  3. The Early Ages

    • Claude Brezinski
    Pages 3-50

  4. The First Steps

    • Claude Brezinski
    Pages 51-75

  5. The Beginning of the Theory

    • Claude Brezinski
    Pages 77-96

  6. Golden Age

    • Claude Brezinski
    Pages 97-140

  7. Maturity

    • Claude Brezinski
    Pages 141-259

  8. The Modern Times

    • Claude Brezinski
    Pages 261-311

  9. Back Matter

    Pages 347-462
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Keywords

About this book

The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great­ est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak­ ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im­ portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran­ scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con­ tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

Authors and Affiliations

  • Laboratoire d’Analyse Numérique et d’Optimisation UFR IEEA-M3, Université des Sciences et Techniques, Villeneuve d’Ascq Cedex, France

    Claude Brezinski

Bibliographic Information

  • Book Title: History of Continued Fractions and Padé Approximants

  • Authors: Claude Brezinski

  • Series Title: Springer Series in Computational Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-58169-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Hardcover ISBN: 978-3-540-15286-6Published: 09 January 1991

  • Softcover ISBN: 978-3-642-63488-8Published: 10 October 2012

  • eBook ISBN: 978-3-642-58169-4Published: 06 December 2012

  • Series ISSN: 0179-3632

  • Series E-ISSN: 2198-3712

  • Edition Number: 1

  • Number of Pages: VIII, 551

  • Topics: Numerical Analysis, Number Theory, Analysis

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