History of Continued Fractions and Padé Approximants

History of Continued Fractions and Padé Approximants
Author :
Publisher : Springer Science & Business Media
Total Pages : 556
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ISBN-10 : 9783642581694
ISBN-13 : 3642581692
Rating : 4/5 (692 Downloads)

Book Synopsis History of Continued Fractions and Padé Approximants by : Claude Brezinski

Download or read book History of Continued Fractions and Padé Approximants written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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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 divis