Skip to main content
SpringerLink
Log in

Some results on separate convergence of continued fractions

  • Chapter
  • First Online:
Computational Methods and Function Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1435))

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

Access this chapter

Log in via an institution
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. R. J. Arms, A. Edrei, The Padé tables and continued fractions generated by totally positive sequences, Mathematical Essays dedicated to A. J. Macintyre, Athens, Ohio (1970), 1–21.

    Google Scholar 

  2. F. W. Atkinson, Discrete and continuous boundary problems, Academic Press, New York, 1964.

    MATH  Google Scholar 

  3. A. Auric, Recherches sur les fractions continues algébriques, J. Math pure et applique, (6) 3 (1907), 105–206.

    MATH  Google Scholar 

  4. A. Edrei, Sur des suites de nombres liées à la théorie des fractions continues, Bull. Sci. Math., (2) 72 (1948), 45–64.

    MathSciNet  MATH  Google Scholar 

  5. Lisa Jacobsen, A note on separate convergence of continued fractions, preprint.

    Google Scholar 

  6. E. Maillet, Sur les fractions continues algébriques, J. Ec. pol., (2) 12 (1908), 41–62.

    MATH  Google Scholar 

  7. O. Perron, Die Lehre von den Kettenbrüchen, 3. Aufl., 2. Band, Teubner, Stuttgart, 1957.

    MATH  Google Scholar 

  8. H.-J. Runckel, Bounded analytic functions in the unit disk and the behavior of certain analytic continued fractions near the singular line, J. reine angew. Math., 281 (1976), 97–125.

    MathSciNet  MATH  Google Scholar 

  9. _____, Continuity on the boundary and analytic continuation of continued fractions, Math. Zeitschr., 148 (1976), 189–205.

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, Meromorphic extension of analytic continued fractions, Rocky Mtn. J. Math., to appear.

    Google Scholar 

  11. J. Schur, Über Potenzreihen die im Innern des Einheitskreises beschränkt sind (Fortsetzung), J. reine angew. Math., 148 (1918/19), 122–145.

    MathSciNet  MATH  Google Scholar 

  12. H. M. Schwartz, A class of continued fractions, Duke Math. J., 6 (1940), 48–65.

    Article  MathSciNet  MATH  Google Scholar 

  13. I. V. Sleshinskii (J. Śleszyński), Convergence of continued fractions (in Russian), Zapiski matematicheskago otodieleniia Novorossiiskago obshchestvoispytatela, 8 (1888), 97–127.

    Google Scholar 

  14. T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8 (1894), 1–122.

    Article  MathSciNet  Google Scholar 

  15. W. J. Thron, Order and type of entire functions arising from separately convergent continued fractions, submitted.

    Google Scholar 

  16. W. J. Thron and H. Waadeland, Convergence questions for limit periodic continued fractions, Rocky Mtn. J. Math., 11 (1981), 641–657.

    Article  MathSciNet  MATH  Google Scholar 

  17. Walter van Assche, Asymptotics for orthogonal polynomials and three term recurrences, Proceedings of Columbus conference, to appear.

    Google Scholar 

  18. H. von Koch, Quelques théorèmes concernant la theorie générale des fractions continues, Översigt av kongl. Vetenskaps-Akademiens Förhandlingar, 52 (1895).

    Google Scholar 

  19. _____, Sur la convergence des determinants d'ordre infini et des fractions continues, Comptes Rendus, 120 (1895), 145.

    Google Scholar 

  20. _____, Sur un théorème de Stieltjes et sur les fonctions définies par des fractions continues, Bull. Soc. Math. France, 23 (1895), 33–41.

    MathSciNet  Google Scholar 

  21. H. Waadeland, A convergence property of certain T-fraction expansions, Kgl. norske videnskabers selskabs skrifter 1966, No. 9, 3–22.

    Google Scholar 

  22. H. S. Wall, Some recent developments in the theory of continued fractions, Bull. Amer. Math. Soc., 47 (1941), 405–423.

    Article  MathSciNet  MATH  Google Scholar 

  23. _____, The behavior of certain Stieltjes continued fractions near the singular line, Bull. Amer. Math. Soc., 48 (1942), 427–431.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Campus Box 426, 80309, Boulder, CO, USA

    W. J. Thron

Authors
  1. W. J. Thron
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Stephan Ruscheweyh Edward B. Saff Luis C. Salinas Richard S. Varga

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Thron, W.J. (1990). Some results on separate convergence of continued fractions. In: Ruscheweyh, S., Saff, E.B., Salinas, L.C., Varga, R.S. (eds) Computational Methods and Function Theory. Lecture Notes in Mathematics, vol 1435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087908

Download citation

  • DOI: https://doi.org/10.1007/BFb0087908

  • Received:

  • Revised:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52768-8

  • Online ISBN: 978-3-540-47139-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation