Continued Fractions

A. Ya. Khinchin

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Paperback

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English

Dover
14 May 1997

Mathematics & Sciences; Probability & statistics

Series: Dover Books on Mathema 1.4tics

In this elementary-level text, eminent Soviet mathematician A. Ya. Khinchin offers a superb introduction to the positive-integral elements of the theory of continued functions, a special algorithm that is one of the most important tools in analysis, probability theory, mechanics, and, especially, number theory. Presented in a clear, straightforward manner, the book comprises three major chapters: the properties of the apparatus, the representation of numbers by continued fractions and the measure theory of continued fractions. The last chapter is somewhat more advanced and deals with the metric, or probability, theory of continued fractions, an important field developed almost entirely by Soviet mathematicians, including Khinchin.

The present volume reprints an English translation of the third Russian edition published in 1961. It is not only an excellent introduction to the study of continued fractions, but a stimulating consideration of the profound and interesting problems of the measure theory of numbers.

By: A. Ya. Khinchin
Imprint: Dover
Country of Publication: United States
Edition: New edition
Dimensions: Height: 215mm, Width: 136mm, Spine: 6mm
Weight: 126g
ISBN: 9780486696300
ISBN 10: 0486696308
Series: Dover Books on Mathema 1.4tics
Pages: 106
Publication Date: 14 May 1997
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Unspecified

Chapter I. Properties of the Apparatus 1. Introduction 2. Convergents 3. Infinite continued fractions 4. Continued fractions with natural elements Chapter II. The Representation of Numbers by Continued Fractions 5. Continued fractions as an apparatus for representing real numbers 6. Convergents as best approximations 7. The order of approximation 8. General approximation theorems 9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers 10. Quadratic irrational numbers and periodic continued fractions Chapter III. The Measure Theory of Continued Fractions 11. Introduction 12. The elements as functions of the number represented 13. Measure-theoretic evaluation of the increase in the elements 14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation 15. Gauss's problem and Kuz'min's theorem 16. Average values Index

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Continued Fractions

A. Ya. Khinchin

$17.95

Paperback

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