History of Continued Fractions and Padé Approximants
Published on 10. October 2012
Book
Paperback/Softback
VIII, 551 pages
978-3-642-63488-8 (ISBN)
Description
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 bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
More details
Series
Edition
Softcover reprint of the original 1st ed. 1991
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 551 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 31 mm
Weight
844 gr
ISBN-13
978-3-642-63488-8 (9783642634888)
DOI
10.1007/978-3-642-58169-4
Schweitzer Classification
Other editions
Additional editions
Claude Brezinski
History of Continued Fractions and Padé Approximants
Book
01/1991
Springer
€235.39
Shipment within 7-9 days
Person
Claude Brezinski is professor emeritus of mathematics at the University of Lille (France), where he has been head of the Laboratory of Numerical Analysis and Optimization for 30 years. He was the advisor of 60 doctoral students. Prof. Brezinski is founder and Editor-in-Chief of the Numerical Algorithms journal and author of over 240 papers and several books.
Michela Redivo-Zaglia is professor of numerical analysis at the University of Padua (Italy). She has been vice-director of the Department of Mathematics for three years. She is a member of the Editorial Board of several journals. She published software packages, 7 scientific and didactic books, and about 80 papers. She was the organizer of many international congresses, and an invited speaker at several more.
Content
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.