Continued Fractions With Applications
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Continued Fractions With Applications
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Author : L. Lorentzen
language : en
Publisher: North Holland
Release Date : 1992-11-08
Continued Fractions With Applications written by L. Lorentzen and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Computers categories.
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.
Metrical Theory Of Continued Fractions
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Author : M. Iosifescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-30
Metrical Theory Of Continued Fractions written by M. Iosifescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-30 with Mathematics categories.
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
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Author : Andrew M Rockett
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-08-08
Continued Fractions written by Andrew M Rockett and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-08 with Mathematics categories.
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.
Neverending Fractions
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Author : Jonathan Borwein
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-03
Neverending Fractions written by Jonathan Borwein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.
Continued Fractions
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Author : Doug Hensley
language : en
Publisher: World Scientific
Release Date : 2006-03-01
Continued Fractions written by Doug Hensley and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.
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.
Handbook Of Continued Fractions For Special Functions
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-12
Handbook Of Continued Fractions For Special Functions written by Annie A.M. Cuyt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-12 with Mathematics categories.
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!
History Of Continued Fractions And Pad Approximants
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Author : Claude Brezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
History Of Continued Fractions And Pad Approximants written by Claude Brezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 ...
The Application Of Continued Fractions And Their Generalizations To Problems In Approximation Theory
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Author : Alekseĭ Nikolaevich Khovanskiĭ
language : en
Publisher:
Release Date : 1963
The Application Of Continued Fractions And Their Generalizations To Problems In Approximation Theory written by Alekseĭ Nikolaevich Khovanskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Approximate computation categories.
Analytic Theory Of Continued Fractions
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Author : Hubert Stanley Wall
language : en
Publisher: Taylor & Francis US
Release Date : 2000
Analytic Theory Of Continued Fractions written by Hubert Stanley Wall and has been published by Taylor & Francis US this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extended discussions of orthogonal polynomials, power series, infinite matrices and quadratic forms in infinitely many variables, definite integrals, the moment problem and the summation of divergent series.
Continued Fractions And Orthogonal Functions
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Author : S. Clement Cooper
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Continued Fractions And Orthogonal Functions written by S. Clement Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
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.