History of Continued Fractions and Padé Approximants

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Springer Science & Business Media, 6 déc. 2012 - 551 pages
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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 ...
 

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Table des matières

INTRODUCTION
1
CHAPTER 2
51
CHAPTER 3
85
CHAPTER 5
136
CHAPTER 6
261
Lalgèbre des géomètres grecs
314
Histoire de lAcadémie Royale des Sciences
320
Elementary Mathematics from an advanced
326
Rapport sur un Mémoire de M Stieltjes
335
Note annexe sur les fractions continues
345
WORKS
463
NAME INDEX
493
SUBJECT INDEX
548
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