Skip to main content

Equimodular limit periodic continued fractions

  • Conference paper
  • First Online:
Analytic Theory of Continued Fractions II

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

The research of N.J. Kalton was supported in part by the National Science Foundation under grant number DMS 8301099. The research of L.J. Lange was supported in part by a grant from the Research Council of the Graduate School, University of Missouri - Columbia and a grant from the Nansen Foundation of Norway.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Christopher Baltus. Limit-Periodic Continued Fractions: Value Regions and Truncation Error Bounds. Ph. D. Thesis, University of Colorado, Boulder, 1984.

    Google Scholar 

  2. A. Elbert, Asymptotic expansion and continued fraction for Mathieu's series, Periodica Mathematica Hungarica 13 (1982) 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  3. Robert Hellar and F.A. Roach. A generalization of a classical necessary condition for convergence of continued fractions. Pac. J. Math. 95 (1981) 307–310.

    Article  MathSciNet  MATH  Google Scholar 

  4. Lisa Jacobsen and Arne Magnus. On the convergence of limit periodic continued fractions K(an/1), where an→−1/4, Lecture Notes in Math., Vol. 1105, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo (1984) 243–248.

    MATH  Google Scholar 

  5. Lisa Jacobsen and Haakon Waadeland, Even and odd parts of limit periodic continued fractions, to appear.

    Google Scholar 

  6. William B. Jones and W.J. Thron, Continued Fractions: Analytic Theory and Applications, Vol. II, Addison-Wesley, Reading, MA, 1980.

    MATH  Google Scholar 

  7. L.J. Lange, σ-Fraction expansions of analytic functions, SIAM J. Math. Anal. 14 (1983) 323–368.

    Article  MathSciNet  MATH  Google Scholar 

  8. Roland Louboutin, Sur un théorème de H. Poincaré relatif aux équations aux differences finies, C.R. Acad. Sc. Paris, t. 299, Serie I, no12, (1984) 539–542.

    MathSciNet  MATH  Google Scholar 

  9. Evar D. Nering, Linear Algebra and Matrix Theory, 2nd. ed., Wiley, New York, 1970.

    MATH  Google Scholar 

  10. Oskar Perron, Die Lehre von den Kettenbrüchen, Band II, Teubner, Stuttgart, 1957.

    MATH  Google Scholar 

  11. W.J. Thron and H. Waadeland, Accelerating convergence of limit periodic continued fractions K(an/1), Num. Math. 34(1980) 155–170.

    Article  MathSciNet  MATH  Google Scholar 

  12. Haakon Waadeland, Tales about tails, Proc. A.M.S. 90 (1984) 57–64.

    Article  MathSciNet  MATH  Google Scholar 

  13. H.S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York, 1948.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Wolfgang J. Thron

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Kalton, N.J., Lange, L.J. (1986). Equimodular limit periodic continued fractions. 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/BFb0075939

Download citation

  • DOI: https://doi.org/10.1007/BFb0075939

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16768-6

  • Online ISBN: 978-3-540-38817-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics