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Some twin regions of convergence for branched continued fractions

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Abstract

We study twin regions of convergence for branched continued fractions and establish an estimate of the rate of convergence; we construct a counterexample showing that the natural formulation of Thron's convergence criterion for continued fractions does not extend to branched continued fractions.

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Literature Cited

  1. D. I. Bodnar,Branched Continued Fractions [in Russian], Naukova Dumka, Kiev (1986).

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  2. W. Jones and W. Thron,Continued Fractions: Analytic Theory and Applications, Addison-Wesley, Reading, MA (1980).

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Authors
  1. G. G. Malachkovs'kii
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Additional information

Translated fromMatematichni Metodi ta Fiziko-Makhanichni Polya, Vol. 39, No. 2, 1996, pp. 62–64.

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Malachkovs'kii, G.G. Some twin regions of convergence for branched continued fractions. J Math Sci 90, 2374–2375 (1998). https://doi.org/10.1007/BF02433969

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  • DOI: https://doi.org/10.1007/BF02433969

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