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A formula of difference for one of the figured approximants of two-dimensional continued fractions

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The present work deals with one of the methods of constructing the figured approximants (figured convergents) for two-dimensional continued fractions, which is used for studying the conditions of equivalence of two two-dimensional continued fractions. The formula of difference for neighboring approximants, which is established in this work, is applied to investigate the properties of a sequence of such figured convergents of two-dimensional continued fractions.

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Authors and Affiliations

  1. “L’vivs’ka Politekhnika” National University, Lviv, Ukraine

    T. M. Antonova

  2. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    O. M. Sus’

Authors
  1. T. M. Antonova
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  2. O. M. Sus’
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 1, pp. 7–18, January–March, 2012.

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Antonova, T.M., Sus’, O.M. A formula of difference for one of the figured approximants of two-dimensional continued fractions. J Math Sci 190, 631–645 (2013). https://doi.org/10.1007/s10958-013-1276-y

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  • DOI: https://doi.org/10.1007/s10958-013-1276-y

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