A Ya Khinchin

Continued Fractions

• Broschiertes Buch

Produktbeschreibung

Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, and more. 1964 edition.

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Produktdetails

• Verlag: Dover Publications
• Revised edition
• Seitenzahl: 112
• Erscheinungstermin: 14. Mai 1997
• Englisch
• Abmessung: 215mm x 137mm x 6mm
• Gewicht: 127g
• ISBN-13: 9780486696300
• ISBN-10: 0486696308
• Artikelnr.: 21750361

Inhaltsangabe

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