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

Part of the Lecture Notes in Mathematics book series (LNM,volume 1199)

Abstract

A previous divergence criterion by A. Magnus and the author is generalized. We show that K(an/1) diverges (by oscillation) if an=−1/4−(c+εn)/n(n+1), where c>1/16 and εn ε ℝ, |ε|=O(1/logαn), α>2.

Keywords

  • Cauchy Sequence
  • Continue Fraction
  • Convergence Region
  • Linear Fractional Transformation
  • Continue Fraction Expansion

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© 1986 Springer-Verlag

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Jacobsen, L. (1986). On the convergence of limit periodic continued fractions K(an/1), where an→−1/4. Part II. In: Thron, W.J. (eds) Analytic Theory of Continued Fractions II. Lecture Notes in Mathematics, vol 1199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075934

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  • DOI: https://doi.org/10.1007/BFb0075934

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16768-6

  • Online ISBN: 978-3-540-38817-3

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