Analytic Theory of Continued Fractions
Analytic Theory of Continued Fractions

Author: Hubert Stanley Wall

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 449

ISBN-13: 0486830446

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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.

Continued Fractions
Continued Fractions

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

Published: 1997-05-14

Total Pages: 116

ISBN-13: 9780486696300

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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.

Metrical Theory of Continued Fractions
Metrical Theory of Continued Fractions

Author: M. Iosifescu

Publisher: Springer Science & Business Media

Published: 2002-09-30

Total Pages: 408

ISBN-13: 9781402008924

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The book is essentially based on recent work of the authors. In order to unify and generalize the results obtained so far, new concepts have been introduced, e.g., an infinite order chain representation of the continued fraction expansion of irrationals, the conditional measures associated with, and the extended random variables corresponding to that representation. Also, such procedures as singularization and insertion allow to obtain most of the continued fraction expansions related to the regular continued fraction expansion. The authors present and prove with full details for the first time in book form, the most recent developments in solving the celebrated 1812 Gauss' problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval. The book is of interest to research workers and advanced Ph.D. students in probability theory, stochastic processes and number theory.

Continued Fractions
Continued Fractions

Author: William B. Jones

Publisher: Cambridge University Press

Published: 2009-02-19

Total Pages: 0

ISBN-13: 9780521101523

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This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.

Analytic Theory of Continued Fractions
Analytic Theory of Continued Fractions

Author: Hubert Stanley Wall

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 449

ISBN-13: 0486823695

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One of the most authoritative and comprehensive books on continued fractions, this monograph presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. 1948 edition.

Continued Fractions: From Analytic Number Theory to Constructive Approximation
Continued Fractions: From Analytic Number Theory to Constructive Approximation

Author: Bruce C. Berndt

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 402

ISBN-13: 0821812009

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This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

CONTINUED FRACTIONS
CONTINUED FRACTIONS

Author: Haakon Waadeland

Publisher: Springer Science & Business Media

Published: 2008-04-01

Total Pages: 321

ISBN-13: 9491216376

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Continued Fractions consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given. This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.

Geometry of Continued Fractions
Geometry of Continued Fractions

Author: Oleg Karpenkov

Publisher: Springer Science & Business Media

Published: 2013-08-15

Total Pages: 409

ISBN-13: 3642393683

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Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.