Geodesic
Leaping convergents of Hurwitz continued fractions
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 101-121

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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_rn+i/q_rn+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 of the leaping convergents for some different types of Hurwitz continued fractions.
Keywords: Leaping convergents, Hurwitz continued fractions 
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Komatsu, Takao. Leaping convergents of Hurwitz continued fractions. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 101-121. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_1_a5/