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References
C. Baltus and W. B. Jones, Truncation error bounds for limit periodic continued fractions with lim an = 0. Numer. Math 46 (1985), 541–569.
P. Henrici and P. Pfluger, Truncation error estimates for Stieltjes fractions. Numer. Math 9 (1966), 120–138.
K. L. Hillam and W. J. Thron, A general convergence criterion for continued fractions K(an/bn), Proc. Amer. Math. Soc. 16 (1965), 1256–1262.
L. Jacobsen, Modified approximants. Construction and applications. Det Kgl. Norske Vit. Selsk. Skr. (1983), No. 3, 1–46.
L. Jacobsen, General convergence of continued fractions. Trans. Amer. Math. Soc., to appear.
L. Jacobsen, A theorem on simple convergence regions for continued fractions K(an/1). These Lecture Notes.
L. Jacobsen, W. B. Jones and H. Waadeland, _____. These Lecture Notes.
W. B. Jones and W. J. Thron, Twin-convergence regions for continued fractions K(an/1), Trans. Amer. Math. Soc. 150 (1970), 93–119.
W. B. Jones and W. J. Thron, Numerical stability in evaluating continued fractions. Math. Comp. 28 (1974), 795–810.
W. B. Jones and W. J. Thron, Truncation error analysis by means of approximant systems and inclusion regions. Numer. Math. 26 (1976), 117–154.
W. 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. Now available through Cambridge Univ. Press.
W. B. Jones, W. J. Thron, and H. Waadeland, Truncation error bounds for continued fractions K(an/1) with parabolic element regions, SIAM J. Numer. Anal. 20 (1983), 1219–1230.
R. E. Lane, The value region problem for continued fractions, Duke Math. J. 12 (1945), 207–216.
W. Leighton and W. J. Thron, Continued fractions with complex elements. Duke Math. J. 9 (1942), 763–772.
G. Loria, Spezielle algebraische und transzendente ebene Kurven, Theorie und Geschichte I, 2. Aufl. B. G. Teubner, Leipzig and Berlin, 1910.
M. Overholt, The values of continued fractions with complex elements, Det Kongelige Norske Vitenskabers Selskabs Skrifter, (1983), No. 1, 109–116.
J. F. Paydon and H. S. Wall, The continued fraction as a sequence of linear transformations. Duke Math. J. 9 (1942), 360–372.
W. M. Reid, Parameterizations and factorizations of element regions for continued fractions K(an/1), Lecture Notes in Mathematics No. 932, Springer-Verlag, Berlin, 1982.
W. M. Reid, Uniform convergence and truncation error estimates of continued fractions K(an/1), Ph.D. thesis, University of Colorado, Boulder, 1978.
W. T. Scott and H. S. Wall, A convergence theorem for continued fractions, Trans. Amer. Math. Soc. 47 (1940), 155–172.
W. T. Scott and H. S. Wall, Value regions for continued fractions, Bull. Amer. Math. Soc. 47 (1941), 580–585.
W. J. Thron and H. Waadeland, Accelerating convergence of limit periodic continued fractions K(an/1), Numer. Math. 34 (1980), 155–170.
J. Worpitzky, Untersuchungen über die Entwickelung der monodromen und monogenen Funktionen durch Kettenbrüche, Jahresbericht, Friedrichs-Gymnasium und Realschule, Berlin, 1865, 3–39.
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Jacobsen, L., Thron, W.J. (1986). Oval convergence regions and circular limit regions for continued fractions K(an/1). 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/BFb0075937
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DOI: https://doi.org/10.1007/BFb0075937
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