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Boundary versions of Worpitzky’s Theorem and of parabola theorems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1406)

Abstract

What happens to the limit regions in Worpitzky’s Theorem and in Parabola Theorems when the element regions are replaced by their boundaries? The present paper gives some answers to such questions.

Keywords

  • Element Region
  • Half Plane
  • Limit Region
  • Continue Fraction
  • Parabolic Element

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References

  1. L. Jacobsen and W. J. Thron, Oval convergence regions and circular limit regions for continued fractions K (a n /1), Analytic Theory of Continued Fractions II (W. J. Thron, Ed.), Lecture Notes in Mathematics 1199, Springer-Verlag, Berlin (1986), 90–126.

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  2. W. B. Jones and W. J. Thron, “Continued fractions: Analytic theory and applications, Encyclopedia of Mathematics and its Applications, 11,” Addison-Wesley, now available from Cambridge University Press, 1980.

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  3. W. B. Jones, W. J. Thron and H. Waadeland, Value regions for continued fractions K(a n /1) whose elements lie in parabolic regions, Math. Scand. 56 (1985), 5–14.

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  4. W. Leighton and W. J. Thron, On value regions of continued fractions, Bull. Amer. Math. Soc. 48, No. 12 (1942), 917–920.

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  5. E. Rye and H. Waadeland, Reflections on value regions, limit regions and truncation errors for continued fractions, Numer. Math. 47 (1985), 191–215.

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

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  7. J. D. T. Worpitzky, Untersuchungen über die Entwickelung der monodromen und monogenen Funktionen durch Kettenbrüche, Friedrichs-Gymnasium und Realschule Jahresbericht, Berlin (1865), 3–39.

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© 1989 Springer-Verlag

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Waadeland, H. (1989). Boundary versions of Worpitzky’s Theorem and of parabola theorems. In: Jacobsen, L. (eds) Analytic Theory of Continued Fractions III. Lecture Notes in Mathematics, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096171

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  • DOI: https://doi.org/10.1007/BFb0096171

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51830-3

  • Online ISBN: 978-3-540-46820-2

  • eBook Packages: Springer Book Archive