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History of continued fractions and Padé approximants

Author: Claude Brezinski
Publisher: Berlin ; New York : Springer-Verlag, ©1991.
Series: Springer series in computational mathematics, 12.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Claude Brezinski
ISBN: 3540152865 9783540152866 0387152865 9780387152868
OCLC Number: 21411454
Description: 551 pages ; 24 cm.
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 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.
Series Title: Springer series in computational mathematics, 12.
Responsibility: Claude Brezinski.
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