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On a certain transformation of continued fractions

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Analytic Theory of Continued Fractions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 932))

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References

  1. John Gill, The use of attractive fixed points in accelerating the convergence of limit-periodic continued fractions, Proc. Amer. Math. Soc. 47 (1975), 119–126.

    Article  MathSciNet  MATH  Google Scholar 

  2. John Gill, Enhancing the convergence region, of a sequence of bilinear transformations, Math. Scand. 43 (1978), 74–80.

    MathSciNet  MATH  Google Scholar 

  3. Lisa Jacobsen, Convergence Acceleration for Continued Fractions K(an/1), Trans. Amer. Math. Soc., to appear.

    Google Scholar 

  4. Lisa Jacobsen, A Method for Convergence Acceleration for Continued Fraction K(an/1), these Lecture Notes.

    Google Scholar 

  5. W.B. Jones and R.I. Snell, Truncation error bounds for continued fractions K(an/1), SIAM J. Numer. Anal. 6 (1969), 210–221.

    Article  MathSciNet  MATH  Google Scholar 

  6. W.B. Jones and W.J. Thron, Numerical stability in evaluating continued fractions, Math. of Comput 28 (1974), 795–810.

    Article  MathSciNet  MATH  Google Scholar 

  7. William B. Jones and Wolfgang J. Thron, Continued fractions: Analytic theory and applications, Encyclopedia of Mathematics and Its Applications, No. 11, Addison-Wesley, Reading, Mass. 1980.

    MATH  Google Scholar 

  8. Tor Leknes, Truncation errors for certain continued fractions, Thesis for the degree cand. real. at the University of Trondheim. In preparation.

    Google Scholar 

  9. O. Perron, Die Lehre von den Kettenbrüchen, Band 2, B.G. Teubner, Stuttgart 1957.

    MATH  Google Scholar 

  10. A. Pringsheim, Über die Konvergenz unendlicher Kettenbrüche. Bayer. Akad. nat. wiss. Kl. Sitzber 28 (1899), 295–324.

    Google Scholar 

  11. W.J. Thron, On parabolic convergence regions for continued fractions, Math. Z. 69 (1958), 173–182.

    Article  MathSciNet  MATH  Google Scholar 

  12. W.J. Thron and Haakon Waadeland, Accelerating convergence of limit periodic continued fractions K(an/1), Numer. Math. 34 (1980), 155–170.

    Article  MathSciNet  MATH  Google Scholar 

  13. W.J. Thron and Haakon Waadeland, Analytic continuation of functions defined by means of continued fractions, Math. Scand. 47 (1980), 72–90.

    MathSciNet  MATH  Google Scholar 

  14. W.J. Thron and Haakon Waadeland, Convergence questions for limit periodic continued fractions, Rocky Mountain J. Math., 11 (1981), 641–657.

    Article  MathSciNet  MATH  Google Scholar 

  15. W.J. Thron and Haakon Waadeland, Survey of Modifications of Continued Fractions, these Lecture Notes.

    Google Scholar 

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Author information

Author notes

  1. W. J. Thron

    Present address: Department of Mathematics, University of Colorado, Campus Box 426, 80309, Boulder, Colorado, U.S.A.

  2. Haakon Waadeland

    Present address: Department of Mathematics and Statistics, University of Trondheim, N-7055, Dragvoll, Norway

Authors and Affiliations

    Authors
    1. W. J. Thron
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    2. Haakon Waadeland
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    Editor information

    William B. Jones W. J. Thron Haakon Waadeland

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    © 1982 Springer-Verlag

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    Thron, W.J., Waadeland, H. (1982). On a certain transformation of continued fractions. In: Jones, W.B., Thron, W.J., Waadeland, H. (eds) Analytic Theory of Continued Fractions. Lecture Notes in Mathematics, vol 932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093316

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    • DOI: https://doi.org/10.1007/BFb0093316

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-11567-0

    • Online ISBN: 978-3-540-39276-7

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