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Continued Fractions With Applications
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Book Synopsis Continued Fractions with Applications by : L. Lorentzen
Download or read book Continued Fractions with Applications written by L. Lorentzen and published by North Holland. This book was released on 1992-11-08 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.
Book Synopsis CONTINUED FRACTIONS by : Haakon Waadeland
Download or read book CONTINUED FRACTIONS written by Haakon Waadeland and published by Springer Science & Business Media. This book was released on 2008-04-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Continued Fractions by : Aleksandr I?Akovlevich Khinchin
Download or read book Continued Fractions written by Aleksandr I?Akovlevich Khinchin and published by Courier Corporation. This book was released on 1997-05-14 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov
Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Metrical Theory of Continued Fractions by : M. Iosifescu
Download or read book Metrical Theory of Continued Fractions written by M. Iosifescu and published by Springer Science & Business Media. This book was released on 2002-09-30 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Continued Fractions and Orthogonal Functions by : S. Clement Cooper
Download or read book Continued Fractions and Orthogonal Functions written by S. Clement Cooper and published by CRC Press. This book was released on 1993-11-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.
Book Synopsis Continued Fractions and Signal Processing by : Tomas Sauer
Download or read book Continued Fractions and Signal Processing written by Tomas Sauer and published by Springer Nature. This book was released on 2021-09-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.
Book Synopsis Neverending Fractions by : Jonathan Borwein
Download or read book Neverending Fractions written by Jonathan Borwein and published by Cambridge University Press. This book was released on 2014-07-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.
Book Synopsis Continued Fractions by : Doug Hensley
Download or read book Continued Fractions written by Doug Hensley and published by World Scientific. This book was released on 2006-03-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.
Book Synopsis Orthogonal Polynomials and Continued Fractions by : S. V. Khrushchev
Download or read book Orthogonal Polynomials and Continued Fractions written by S. V. Khrushchev and published by . This book was released on 2008 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum."--Publisher's description.
Book Synopsis Handbook of Continued Fractions for Special Functions by : Annie A.M. Cuyt
Download or read book Handbook of Continued Fractions for Special Functions written by Annie A.M. Cuyt and published by Springer Science & Business Media. This book was released on 2008-04-12 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!
Book Synopsis Continued Fractions by : William B. Jones
Download or read book Continued Fractions written by William B. Jones and published by Cambridge University Press. This book was released on 2009-02-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.
Book Synopsis Continued Fractions by : Andrew M Rockett
Download or read book Continued Fractions written by Andrew M Rockett and published by World Scientific Publishing Company. This book was released on 1992-08-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Book Synopsis Multidimensional Continued Fractions by : Fritz Schweiger
Download or read book Multidimensional Continued Fractions written by Fritz Schweiger and published by Oxford University Press, USA. This book was released on 2000 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematician Fritz Schweiger, whose academic affiliation is not provided, provides an introduction to a field of research that has seen remarkable progress in recent decades, concentrating on multidimensional continued fractions which can be described by fractional linear maps or equivalently by a set of (n + 1) x (n + 1) matrices. Addressing the question of periodicity, he refines the problem of convergence to the question of whether these algorithms give "good" simultaneous Diophantine approximations. He notes that these algorithms are not likely to provide such "good" approximations which satisfy the n-dimensional Dirichlet property. Also studied are the ergodic properties of these maps. Annotation copyrighted by Book News Inc., Portland, OR
Book Synopsis Analytic Theory of Continued Fractions by : Hubert Stanley Wall
Download or read book Analytic Theory of Continued Fractions written by Hubert Stanley Wall and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elements of Number Theory by : I. M. Vinogradov
Download or read book Elements of Number Theory written by I. M. Vinogradov and published by Courier Dover Publications. This book was released on 2016-01-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, detailed exposition that can be understood by readers with no background in advanced mathematics. More than 200 problems and full solutions, plus 100 numerical exercises. 1949 edition.
Book Synopsis Orthogonal Functions by : William Jones
Download or read book Orthogonal Functions written by William Jones and published by CRC Press. This book was released on 2020-12-22 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."
