Akovlevich Khinchin , Herbert Eagle Courier Corporation , May 14, - Mathematics - 95 pages 0 Reviews Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Continued fractions Mathematical constants. Classical and Quantum Computation Alexei Yu. Continued Fractions Aleksandr I? Since the first coefficient a 0 of the continued fraction of x plays no role in Khinchin's theorem and since the rational numbers have Lebesgue measure zero, we are reduced to the study of irrational numbers in the unit interval , i. This is obtained by taking the p -th mean in conjunction with the Gauss—Kuzmin distribution. Retrieved from " https: 
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Taking the khinchim on both sides, we obtain to the left the geometric mean of the first n coefficients of the continued fraction, and to the right Khinchin's constant. All articles with unsourced statements Articles with unsourced statements from August CS1 errors: Courier CorporationMay 14, - Mathematics - 95 pages. In number theoryAleksandr Yakovlevich Khinchin proved that for almost all real numbers xcoefficients a i of the continued fraction expansion of x have a finite geometric mean that is independent of the value of x and is known as Khinchin's constant.
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Continued Fractions - Aleksandr I?Akovlevich Khinchin, Herbert Eagle - Google Books
Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. In other projects Wikimedia Commons.
Views Read Edit View history. KitaevAlexander ShenMikhail N. Continued fractions Mathematical constants. By means of the above expressions, the harmonic mean of the terms of a continued fraction may be obtained as well. Akovlevich KhinchinHerbert Eagle Limited preview - The transformation T is called the Gauss—Kuzmin—Wirsing operator.
Khinchin's constant
Contents Chapter I Properties of the Apparatus. Khinchin's constant may be expressed as a rational zeta series in the form. Continued Fractions Aleksandr I? Chapter I Properties of the Apparatus.
Playing with continued fractions and Khinchin’s constant
Define a transformation T: Continued Fractions Dover books on mathematics. From Wikipedia, the free encyclopedia.
Vyalyi No preview available - Although almost all numbers satisfy this property, it has not been proven for any real number not specifically constructed for the purpose. Read, highlight, and take notes, across web, tablet, and phone. The value obtained is. Account Options Sign in. Selected pages Rfactions Page.
This is obtained by taking the p -th mean in conjunction fraactions the Gauss—Kuzmin distribution. Retrieved from " https: Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Classical and Quantum Computation Alexei Yu.
Khinchin's constant - Wikipedia
An expansion may also be given in terms of the dilogarithm:. My library Help Advanced Book Search. By contniued this site, you agree to the Terms of Use and Privacy Policy. Akovlevich KhinchinHerbert Eagle Courier CorporationMay 14, - Mathematics - 95 pages 0 Reviews Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions.
This page was last continufd on 19 Julyat Since the first coefficient a 0 of the continued fraction of x plays no role in Khinchin's theorem and since the rational numbers have Lebesgue measure zero, we are reduced to the study of irrational numbers in the unit intervali.
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