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Convergence of two-dimensional continued fractions with complex elements

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Abstract

We prove an analog of Vorpits'kii's theorem for two-dimensional continued fractions, applying the formulas for computing their absolute error.

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Literature Cited

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

    Google Scholar 

  2. D. I. Bodnar, H. Waadeland, Kh. I. Kuchmins'ka, and O. M. Sus', “On the stability of branched continued fractions,”Mat. Met. Fiz.-Mekh. Polya, No. 37, 3–7 (1994).

    Google Scholar 

  3. D. I. Bodnar and Kh. I. Kuchminskaya, “On the convergence of the expansion of a function of two variables into a corresponding branched continued fraction,”Mat. Met. Fiz.-Mekh. Polya, No. 11, 3–6 (1980)

    MATH  Google Scholar 

  4. W. Jones and W. Thron,Continued Fractions, Addison-Wesley, Reading, MA (1980).

    Google Scholar 

  5. L. Lorentzen and H. Waadeland,Continued Fractions with Applications, North-Holland, Amsterdam (1992).

    Google Scholar 

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Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 75–83.

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Sus', O.M. Convergence of two-dimensional continued fractions with complex elements. J Math Sci 90, 2385–2392 (1998). https://doi.org/10.1007/BF02433972

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  • DOI: https://doi.org/10.1007/BF02433972

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