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

  • Lisa Jacobsen
  • Arne Magnus
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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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Lisa Jacobsen
    • 1
  • Arne Magnus
    • 2
  1. 1.Matematisk Institutt NLHT TrondheimNorway
  2. 2.Department of MathematicsColorado State UniversityFt. CollinsUSA

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