History of Continued Fractions and Padé Approximants

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