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

Convergence Theory

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Real Axis
  • Duke Math
  • Continue Fraction
  • Convergence Region
  • Closed Disk

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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

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