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2011 | 31 | 1 | 101-121
Tytuł artykułu

Leaping convergents of Hurwitz continued fractions

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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.
Twórcy
  • Graduate School of Science and Technology Hirosaki University, Hirosaki, 036-8561, Japan
Bibliografia
  • [1] C. Elsner, On arithmetic properties of the convergents of Euler's number, Colloq. Math. 79 (1999), 133-145.
  • [2] C. Elsner and T. Komatsu, A recurrence formula for leaping convergents of non-regular continued fractions, Linear Algebra Appl. 428 (2008), 824-833. doi: 10.1016/j.laa.2007.08.011
  • [3] T. Komatsu, Recurrence relations of the leaping convergents, JP J. Algebra Number Theory Appl. 3 (2003), 447-459.
  • [4] T. Komatsu, Arithmetical properties of the leaping convergents of $e^{1/s}$, Tokyo J. Math. 27 (2004), 1-12. doi: 10.3836/tjm/1244208469
  • [5] T. Komatsu, Some combinatorial properties of the leaping convergents, p. 315-325 in: Combinatorial Number Theory, 'Proceedings of the Integers Conference 2005 in Celebration of the 70th Birthday of Ronald Graham', Carrollton, Georgia, USA, October 27-30, 2005, eds. by B.M. Landman, M.B. Nathanson, J. Nesetril, R.J. Nowakowski and C. Pomerance, Walter de Gruyter 2007.
  • [6] T. Komatsu, Some combinatorial properties of the leaping convergents, II, Applications of Fibonacci Numbers, Proceedings of 12th International Conference on Fibonacci Numbers and their Applications', Congr. Numer. 200 (2010), 187-196.
  • [7] T. Komatsu, Hurwitz continued fractions with confluent hypergeometric functions, Czech. Math. J. 57 (2007), 919-932. doi: 10.1007/s10587-007-0085-1
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1177
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