Analytic Theory Of Continued Fractions Ii
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| Author | : Hubert Stanley Wall |
| Publisher | : Courier Dover Publications |
| Total Pages | : 449 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830446 |
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 | : Wolfgang J. Thron |
| Publisher | : Springer |
| Total Pages | : 305 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540388176 |
| Author | : Aleksandr I?Akovlevich Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 116 |
| Release | : 1997-05-14 |
| Genre | : Mathematics |
| ISBN | : 9780486696300 |
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 | : M. Iosifescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 408 |
| Release | : 2002-09-30 |
| Genre | : Mathematics |
| ISBN | : 9781402008924 |
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.
| Author | : William B. Jones |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2009-02-19 |
| Genre | : Mathematics |
| ISBN | : 9780521101523 |
This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.
| Author | : Lisa Jacobsen |
| Publisher | : Springer |
| Total Pages | : 152 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354046820X |
| Author | : Hubert Stanley Wall |
| Publisher | : Courier Dover Publications |
| Total Pages | : 449 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486823695 |
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.
| Author | : Bruce C. Berndt |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 402 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821812009 |
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.
| Author | : L. Lorentzen |
| Publisher | : North Holland |
| Total Pages | : 634 |
| Release | : 1992-11-08 |
| Genre | : Computers |
| ISBN | : |
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.
| Author | : Haakon Waadeland |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2008-04-01 |
| Genre | : Mathematics |
| ISBN | : 9491216376 |
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.
