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Transactions of the American Mathematical Society

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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
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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, New York, 1979. MR 510197 (80c:30001)
  • [2] Marcel G. de Bruin and Lisa Jacobsen, The dominance concept for linear recurrence relations with applications to continued fractions (to appear).
  • [3] H. Hamburger, Über eine Erweiterung des Stieltjesschen Momentproblems. I, Math. Ann. 81 (1920), 235-319. MR 1511966
  • [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 W. J. Thron, Continued fractions. Analytic theory and applications, Encyclopedia of Mathematics and its applications, Vol. 11, Addison-Wesley, Reading, Mass., 1980. MR 595864 (82c:30001)
  • [7] Oskar Perron, Die Lehre von den Kettenbrüchen, Bd. II, Teubner, Stuttgart, 1957. MR 0085349 (19:25c)
  • [8] W. J. Thron and Haakon Waadeland, Modifications of continued fractions. A survey, Lecture Notes in Math., vol. 932, Springer-Verlag, Berlin and New York, 1982, pp. 38-66. MR 690452 (84j:30013)
  • [9] Haakon Waadeland, Tales about tails, Proc. Amer. Math. Soc. 90 (1984), 57-64. MR 722415 (85f:40003)

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Keywords: Continued fractions, convergence, modified approximants
Article copyright: © Copyright 1986 American Mathematical Society

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