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History of Continued Fractions and Pade Approximants : Springer Series in Computational Mathematics - C. Brezinski

History of Continued Fractions and Pade Approximants

Springer Series in Computational Mathematics

Hardcover

Published: December 1990
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The concept of continued fractions os one of the oldest in the history of mathematics. It can be traced back to Euclid's algorithm for the greatest common divisor or even earlier. Continued fractions and Pade approximants played an important role in the development of many branches of mathematics, such as the spectral theory of operators, and in the solution of famous problems, such as the quadrature of the circle.

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 Pade approximants.- 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 Pade approximants.- 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 Pade approximants.- 6.5 Extensions and applications.- Documents.- Document 1: L'algebre des geometres grecs.- Document 2: Histoire de l'Academie Royale des Sciences.- Document 3: Encyclopedie (Supplement).- Document 4: Elementary Mathematics from an advanced standpoint.- Document 5: Sur quelques applications des fractions continues.- Document 6: Rapport sur un Memoire 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.

ISBN: 9783540152866
ISBN-10: 3540152865
Series: Springer Series in Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 551
Published: December 1990
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.77 x 16.51  x 3.81
Weight (kg): 0.96