History of Continued Fractions and Padé Approximants
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 bourgeoi...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1991, 1991
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| Edition: | 1st ed. 1991 |
| Series: | Springer Series in Computational Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 The Early Ages
- 1.1 Euclid’s algorithm
- 1.2 The square root
- 1.3 Indeterminate equations
- 1.4 History of notations
- 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
- 3 The Beginning of the Theory
- 3.1 Brouncker and Wallis
- 3.2 Huygens
- 3.3 Number theory
- 4 Golden Age
- 4.1 Euler
- 4.2 Lambert
- 4.3 Lagrange
- 4.4 Miscellaneous contributions
- 4.5 The birth of Padé approximants
- 5 Maturity
- 5.1 Arithmetical continued fractions
- 5.2 Algebraic continued fractions
- 5.3 Varia
- 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
- 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
- Document 8: Notice sur les travaux et titres
- Document 9: Note annexe sur les fractions continues
- Scientific Bibliography
- Works
- Historical Bibliography
- Name Index