Continued FractionsCourier Corporation, 14.05.1997 - 95 Seiten Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral 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. |
Inhalt
Chapter I Properties of the Apparatus | 1 |
Chapter II The Representation of Numbers | 16 |
Chapter III The Measure Theory of Continued Fractions | 51 |
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Häufige Begriffe und Wortgruppen
a₁ a₂ algebraic number an+1 apparatus of continued assertion basis of Theorem best approximation CALCULUS OF VARIATIONS canonical representation completes the proof consequently continued frac continued fraction 13 continued fraction representing convergent of order countable set defined denote Edwards Deming equation everywhere finite continued fraction finite number follows formula fraction a/b function given continued fraction hence infinite set intermediate fractions interval Jn interval of rank k₁ lemma Let us agree Liouville's theorem measure theory measure zero mediant natural number obtain obviously odd-order convergent order of approximation p/qk periodic continued fraction pk/qk positive number problem proof of Theorem properties proves quadratic irrational number r₁ rational fractions rational number real number satisfy the inequality second kind sequence set of numbers solutions in integers sufficiently large Suppose Theorem 15 Theorem 33 Theorem 9 theory of continued tinued fraction tion
Verweise auf dieses Buch
Classical and Quantum Computation Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi Keine Leseprobe verfügbar - 2002 |