History of Continued Fractions and Padé Approximants

  • Claude Brezinski

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Claude Brezinski
    Pages 1-2
  3. Claude Brezinski
    Pages 3-50
  4. Claude Brezinski
    Pages 51-75
  5. Claude Brezinski
    Pages 77-96
  6. Claude Brezinski
    Pages 97-140
  7. Claude Brezinski
    Pages 141-259
  8. Claude Brezinski
    Pages 261-311
  9. Back Matter
    Pages 347-462

About this book

Introduction

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 ...

Keywords

Geschichte der Mathematik History of Mathematics Pade Approximation Zahlentheorie differential equation number theory orthogonal polynomials

Authors and affiliations

  • Claude Brezinski
    • 1
  1. 1.Laboratoire d’Analyse Numérique et d’Optimisation UFR IEEA-M3Université des Sciences et TechniquesVilleneuve d’Ascq CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58169-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63488-8
  • Online ISBN 978-3-642-58169-4
  • Series Print ISSN 0179-3632
  • About this book