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Continued Fractions / A Ya Khinchinvv

By: Khinchin, A. YaContributor(s): Khinchin, A. YaMaterial type: Text

TextPublisher number: :Technical Bureau India Pvt. Ltd. | :E/261, Shastri Nagar DelhiPublication details: New .York ;Dover Publications, 1997Description: xi, 95 pages : illustrations ; 22 cmISBN: 9780486696300Subject(s): Mathematics | Continued fractions | Fractions continuesDDC classification: 517.21 KHI

Contents:

1. Properties of the apparatus. Convergents -- Infinite continued fractions -- Continued fractions with natural elements. 2. The representation of numbers by continued fractions. Continued fractions as an apparatus for representing real numbers -- Convergents as best approximations -- The order of approximation -- General approximation theorems -- The approximation of algebraic irrational numbers and Liouville's transcendental numbers -- Quadratic irrational numbers and periodic continued fractions. 3. The measure theory of continued fractions. The elements as functions of the number represented -- Measure-theoretic evaluation of the increase in the elements -- Measure-theoretic evaluation of the increase in the: elements; denominators of the convergents -- Gauss's problem and Kuz'min's theorem -- Average values.

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Item type	Current library	Call number	Status	Notes	Date due	Barcode	Item holds
Mathematics Departmental Library	Mathematics Departmental Library	517.21 KHI (Browse shelf(Opens below))	Not For Loan	FPDA Grant		M363

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Previous	517 LEC Élements de calcul différential et intégral.	517 RUD Principles of mathematical analysis	517.2 NAR A text book of Cartesian tensors	517.21 KHI Continued Fractions	517.3 NAC The Haar integral	517.35 WIE The Fourier integral, and certain of its applications	517.36 HAN Elliptic integrals	Next

1. Properties of the apparatus. Convergents --
Infinite continued fractions --
Continued fractions with natural elements. 2. The representation of numbers by continued fractions. Continued fractions as an apparatus for representing real numbers --
Convergents as best approximations --
The order of approximation --
General approximation theorems --
The approximation of algebraic irrational numbers and Liouville's transcendental numbers --
Quadratic irrational numbers and periodic continued fractions. 3. The measure theory of continued fractions. The elements as functions of the number represented --
Measure-theoretic evaluation of the increase in the elements --
Measure-theoretic evaluation of the increase in the: elements; denominators of the convergents --
Gauss's problem and Kuz'min's theorem --
Average values.

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