# Leaping convergents of Tasoev continued fractions

Discussiones Mathematicae - General Algebra and Applications (2011)

- Volume: 31, Issue: 2, page 201-216
- ISSN: 1509-9415

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topTakao Komatsu. "Leaping convergents of Tasoev continued fractions." Discussiones Mathematicae - General Algebra and Applications 31.2 (2011): 201-216. <http://eudml.org/doc/276577>.

@article{TakaoKomatsu2011,

abstract = {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 $p_\{rn+i\}/q_\{rn+i\}$ (n=0,1,2,...) for fixed integers r ≥ 2 and 0 ≤ i ≤ r-1.},

author = {Takao Komatsu},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {leaping convergents; Tasoev continued fractions},

language = {eng},

number = {2},

pages = {201-216},

title = {Leaping convergents of Tasoev continued fractions},

url = {http://eudml.org/doc/276577},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Takao Komatsu

TI - Leaping convergents of Tasoev continued fractions

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2011

VL - 31

IS - 2

SP - 201

EP - 216

AB - 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 $p_{rn+i}/q_{rn+i}$ (n=0,1,2,...) for fixed integers r ≥ 2 and 0 ≤ i ≤ r-1.

LA - eng

KW - leaping convergents; Tasoev continued fractions

UR - http://eudml.org/doc/276577

ER -

## References

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- [18] B.G. Tasoev, Rational approximations to certain numbers (Russian), Mat. Zametki 67 (2000), 931-937; English transl. in Math. Notes 67 (2000), 786-791.

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