Skip to main content
SpringerLink
Log in

Estimates of the Rate of Pointwise and Uniform Convergence for One-Periodic Branched Continued Fractions of a Special Form

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

A new formula for the difference between two approximants of one-periodic branched continued fractions of a special form is constructed. An estimate for the rate of pointwise and uniform convergence of fractions of this sort is obtained with the help of this formula.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Bodnar and M. Bubnyak, “On the convergence of 1-periodic branched continued fractions of a special form,” Mat. Visn. NTSh., 8, 5–16 (2011).

    MATH  Google Scholar 

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

    Google Scholar 

  3. C. Brezinski, History of Continued Fractions and Padé Approximants, Springer, Berlin (1991), Springer Ser. in Computational Mathematics, Vol. 12.

  4. A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland, and W. B. Jones, Handbook of Continued Fractions for Special Functions, Springer, New York (2008).

    MATH  Google Scholar 

  5. W. B. Jones and W. J. Thron, Continued Fractions: Analytic Theory and Applications, Addison-Wesley, Reading, MA (1980), Encyclopedia of Mathematics and its Applications, Edited by G.-C. Rota, Vol. 11.

  6. L. Lorentzen and H. Waadeland, Continued Fractions, Vol. 1, Convergence Theory, Atlantis Press/World Scientific, Amsterdam–Paris (2008)

    Book  MATH  Google Scholar 

  7. O. Perron, Die Lehre von der Kettenbrüchen, Band II, Analytisch-Funktionen Theoretishe Kettenbrüche, Teubner, Stuttgart (1957).

  8. W. J. Thron and H. Waadeland, “Modifications of continued fractions. A survey,” in: Analytic Theory of Continued Fractions, Springer, Berlin (1981), Lect. Notes in Math., 932, 38–66.

  9. H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York (1948).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ternopil’ National Economic University, Ternopil’, Ukraine

    D. I. Bodnar & M. M. Bubnyak

Authors
  1. D. I. Bodnar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Bubnyak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 4, pp. 24–32, October–December, 2013.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bodnar, D.I., Bubnyak, M.M. Estimates of the Rate of Pointwise and Uniform Convergence for One-Periodic Branched Continued Fractions of a Special Form. J Math Sci 208, 289–300 (2015). https://doi.org/10.1007/s10958-015-2446-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2446-x

Keywords

Search

Navigation