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Continued Fractions 3RD Editionby Aleksandr Khinchin
Synopses & ReviewsPublisher Comments:Elementarylevel text by noted Soviet mathematician offers superb introduction to positiveintegral 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. Synopsis:Elementarylevel text by noted Soviet mathematician offers superb introduction to positiveintegral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, more. 1964 edition. Table of ContentsChapter 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. Measuretheoretic evaluation of the increase in the elements 14. Measuretheoretic 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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