Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

General convergence of continued fractions


Author: Lisa Jacobsen
Journal: Trans. Amer. Math. Soc. 294 (1986), 477-485
MSC: Primary 40A15; Secondary 30B70
MathSciNet review: 825716
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a new concept of convergence of continued fractions--general convergence. Moreover, we compare it to the ordinary convergence concept and to strong convergence. Finally, we prove some properties of general convergence.


References [Enhancements On Off] (What's this?)

  • [1] Lars V. Ahlfors, Complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable; International Series in Pure and Applied Mathematics. MR 510197
  • [2] Marcel G. de Bruin and Lisa Jacobsen, The dominance concept for linear recurrence relations with applications to continued fractions (to appear).
  • [3] Hans Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 81 (1920), no. 2-4, 235–319 (German). MR 1511966, 10.1007/BF01564869
  • [4] G. Hamel, Über einen limitärperiodischen Kettenbruch, Arch. Math. Phys. 27 (1918), 37-43.
  • [5] Lisa Jacobsen, Modified approximants for continued fractions. Construction and applications, Det Kgl. Norske Vid. Selsk. Skr. No. 3 (1983), 1-46.
  • [6] William B. Jones and Wolfgang J. Thron, Continued fractions, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980. Analytic theory and applications; With a foreword by Felix E. Browder; With an introduction by Peter Henrici. MR 595864
  • [7] Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957 (German). MR 0085349
  • [8] W. J. Thron and Haakon Waadeland, Modifications of continued fractions, a survey, Analytic theory of continued fractions (Loen, 1981) Lecture Notes in Math., vol. 932, Springer, Berlin-New York, 1982, pp. 38–66. MR 690452
  • [9] Haakon Waadeland, Tales about tails, Proc. Amer. Math. Soc. 90 (1984), no. 1, 57–64. MR 722415, 10.1090/S0002-9939-1984-0722415-5

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 40A15, 30B70

Retrieve articles in all journals with MSC: 40A15, 30B70


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825716-1
Keywords: Continued fractions, convergence, modified approximants
Article copyright: © Copyright 1986 American Mathematical Society