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On the convergence of limit periodic continued fractions K(an/1), where a1 → −1/4

  • Convergence Theory
  • Conference paper
  • First Online:
Rational Approximation and Interpolation

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1105))

Abstract

It is well known that the continued fraction K(an/1), where an → −1/4, converges, provided |an+1/4| ≦ 1/16n(n+1) for all n. We show that the constant 1/16 is best possible in the sense that if an=−1/4 – c/n(n+1), where c>1/16 then K(an/1) diverges by oscillation.

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References

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Author information

Authors and Affiliations

  1. Matematisk Institutt NLHT Trondheim, Norway

    Lisa Jacobsen

  2. Department of Mathematics, Colorado State University, 80523, Ft. Collins, Colorado, USA

    Arne Magnus

Authors
  1. Lisa Jacobsen
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  2. Arne Magnus
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Editor information

Peter Russell Graves-Morris Edward B. Saff Richard S. Varga

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© 1984 Springer-Verlag

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Jacobsen, L., Magnus, A. (1984). On the convergence of limit periodic continued fractions K(an/1), where a1 → −1/4. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072415

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  • DOI: https://doi.org/10.1007/BFb0072415

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

  • eBook Packages: Springer Book Archive

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