Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 3642581692
Category : Mathematics
Languages : en
Pages : 556
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Book 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 ...
Author: Hubert Stanley Wall
Publisher: Courier Dover Publications
ISBN: 0486830446
Category : Mathematics
Languages : en
Pages : 449
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Book Description
One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful. The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.
Author: Meyer Hirsch
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 362
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Book Description
Author: Horatio Nelson Robinson
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 468
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Book Description
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486696300
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.
Author: H. Davenport
Publisher: Cambridge University Press
ISBN: 1139643525
Category : Mathematics
Languages : en
Pages : 265
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Book Description
The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers and number theory, and primality testing. Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.
Author: Jonathan Borwein
Publisher: Cambridge University Press
ISBN: 0521186498
Category : Mathematics
Languages : en
Pages : 223
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Book Description
This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.
Author: Folke Ryde
Publisher:
ISBN:
Category : Continued fractions
Languages : en
Pages : 516
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Book Description
Author: Andrzej Schinzel
Publisher: European Mathematical Society
ISBN: 9783037190388
Category : Analyse diophantienne
Languages : en
Pages : 554
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Book Description
Author: Jürgen Sander
Publisher: Springer
ISBN: 3319282034
Category : Mathematics
Languages : en
Pages : 552
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Book Description
This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.
