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Continued Fractions

1997-05-14 Mathematics
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Release : 1997-05-14
Genre : Mathematics
Kind : eBook
Book Rating : 300/5 ( reviews)

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Book Synopsis Continued Fractions by : Aleksandr I?Akovlevich Khinchin

Download or read book Continued Fractions written by Aleksandr I?Akovlevich Khinchin. This book was released on 1997-05-14. 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.

Continued Fractions

1992-08-08 Mathematics
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Release : 1992-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 418/5 ( reviews)

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Book Synopsis Continued Fractions by : Andrew M Rockett

Download or read book Continued Fractions written by Andrew M Rockett. This book was released on 1992-08-08. 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.

Geometry of Continued Fractions

2013-08-15 Mathematics
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Release : 2013-08-15
Genre : Mathematics
Kind : eBook
Book Rating : 683/5 ( reviews)

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Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov. This book was released on 2013-08-15. 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.

Handbook of Continued Fractions for Special Functions

2008-04-12 Mathematics
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Release : 2008-04-12
Genre : Mathematics
Kind : eBook
Book Rating : 499/5 ( reviews)

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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. This book was released on 2008-04-12. 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!

Metrical Theory of Continued Fractions

2002-09-30 Mathematics
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Release : 2002-09-30
Genre : Mathematics
Kind : eBook
Book Rating : 924/5 ( reviews)

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Book Synopsis Metrical Theory of Continued Fractions by : M. Iosifescu

Download or read book Metrical Theory of Continued Fractions written by M. Iosifescu. This book was released on 2002-09-30. 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.

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