Continued FractionsUniversity of Chicago Press, 1964 - 95 Seiten |
Inhalt
Chapter I Properties of the Apparatus | 1 |
Chapter II The Representation of Numbers | 16 |
Chapter III The Measure Theory of Continued Fractions | 51 |
Urheberrecht | |
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a₁ a₂ algebraic number an+1 apparatus of continued assertion basis of Theorem best approximation completes the proof consequently continued frac continued fraction 13 continued fraction representing convergent of order countable set defined denote equation everywhere finite continued fraction finite number follows formula fraction a/b function G₁ 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 Richmond Lattimore rn+1 satisfy the inequality second kind sequence set of numbers solutions in integers sufficiently large Suppose T. V. Smith Theorem 29 Theorem 33 theory of continued tinued fraction tion