History of Continued Fractions and Padé Approximants

Description

Title page INTRODUCTION CHAPTER 1: THE EARLY AGES 1.1 Euclid's algorithm 1.2 The square root 1.3 Indeterminate equations 1.4 History of notations CHAPTER 2: THE FIRST STEPS 2.1 Ascending continued fractions 2.2 The birth of continued fractions 2.3 Miscellaneous contributions 2.4 Pell's equation CHAPTER 3: THE BEGINNING OF THE THEORY 3.1 Brouncker and Wallis 3.2 Huygens 3.3 Number theory CHAPTER 4: GOLDEN AGE 4.1 Euler 4.2 Lambert 4.3 Lagrange 4.4 Miscellaneous contributions 4.5 The birth of Padé approximants CHAPTER 5: MATURITY 5.1 Arithmetical continued fractions 5.1.1 Algebraic properties 5.1.2 Arithmetic 5.1.3 Applications 5.1.4 Number theory 5.1.5 Convergence 5.2 Algebraic continued fractions 5.2.1 Expansion methods and properties 5.2.2 Examples and applications 5.2.3 Orthogonal polynomials 5.2.4 Convergence and analytic theory 5.2.5 Padé approximants 5.3 Varia CHAPTER 6: THE MODERN TIMES 6.1 Number theory 6.2 Set and probability theories 6.3 Convergence and analytic theory 6.4 Padé approximants 6.5 Extensions and applications APPENDIX DOCUMENTS Document 1: L'algèbre des géomètres grecs Document 2: Histoire de l'Académie Royale des Sciences Document 3: Encyclopédie (Supplément) Document 4: Elementary Mathematics from an advanced standpoint Document 5: Sur quelques applications des fractions continues Document 6: Rapport sur un Mémoire de M. Stieltjes Document 7: Correspondance d'Hermite et de Stieltjes Doèument 8: Notice sur les travaux et titres Document 9: Note annexe sur les fractions continues SCIENTIFIC BIBLIOGRAPHY WORKS HISTORICAL BIBLIOGRAPHY NAME INDEX SUBJECT INDEX