Displaying similar documents to “On the length of the continued fraction for values of quotients of power sums”

Leaping convergents of Hurwitz continued fractions

Takao Komatsu (2011)

Discussiones Mathematicae - General Algebra and Applications

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Let pₙ/qₙ = [a₀;a₁,...,aₙ] be the n-th convergent of the continued fraction expansion of [a₀;a₁,a₂,...]. Leaping convergents are those of every r-th convergent p r n + i / q r n + i (n = 0,1,2,...) for fixed integers r and i with r ≥ 2 and i = 0,1,...,r-1. The leaping convergents for the e-type Hurwitz continued fractions have been studied. In special, recurrence relations and explicit forms of such leaping convergents have been treated. In this paper, we consider recurrence relations and explicit forms...

Leaping convergents of Tasoev continued fractions

Takao Komatsu (2011)

Discussiones Mathematicae - General Algebra and Applications

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Denote the n-th convergent of the continued fraction by pₙ/qₙ = [a₀;a₁,...,aₙ]. We give some explicit forms of leaping convergents of Tasoev continued fractions. For instance, [0;ua,ua²,ua³,...] is one of the typical types of Tasoev continued fractions. Leaping convergents are of the form p r n + i / q r n + i (n=0,1,2,...) for fixed integers r ≥ 2 and 0 ≤ i ≤ r-1.