Download or read book History of Continued Fractions and Pad 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 ...

Download or read book Continued Fractions and Pad Approximants written by Claude Brezinski and published by North Holland. This book was released on 1990 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Padeacute; approximants and continued fractions are typical examples of old areas of mathematics (continued fractions can be traced back to Euclid's g.c.d. algorithm more than 2000 years ago) which are again very much alive. This is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital filtering, signal processing, fractals, fluid mechanics, theoretical physics, chemistry, engineering etc. This renewal of interest is also due to their intimate connection with other important topics such as orthogonal polynomials (another old subject now again in full vitality), rational approximation, Gaussian quadratures, extrapolation and convergence acceleration methods, differential equations etc.

Download or read book History of Continued Fractions and Pad Approximants written by Claude Brezinski and published by Springer Verlag. This book was released on 1991 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 divisor or even earlier. Continued fractions and Pade approximants played an important role in the development of many branches of mathematics, such as the spectral theory of operators, and in the solution of famous problems, such as the quadrature of the circle.

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.

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.

Download or read book Continued Fractions written by Carl Douglas Olds and published by Mathematical Association of America (MAA). This book was released on 1963 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Bibliography on Continued Fractions Pad Approximation Sequence Transformation and Related Subjects written by Claude Brezinski and published by . This book was released on 1991 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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!

Download or read book PADE APPROXIMANTS CONTINUED FRACTIONS AND RELATED TOPICS PROCEEDINGS OF THE INTERNATIONAL CONFERENCE written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Continued Fractions written by A. M. Rockett and published by World Scientific. This book was released on 1992-08-01 with total page 202 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.

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

Download or read book Continued Fractions written by Doug Hensley and published by World Scientific. This book was released on 2006 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction to the history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context.

Download or read book Continued Fractions written by Leo Jerome Lange and published by American Mathematical Soc.. This book was released on 1999-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Pade 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.

Download or read book Pade Approximants and Continued Fractions written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Pad Approximants Associated with the Continued Fraction and Series of Stieltjes written by Hubert Stanley Wall and published by . This book was released on 1929 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Continued fractions and Pade approximants written by C. Brezinski and published by . This book was released on 1990 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 114 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.