Tales about tails
Author:
Haakon Waadeland
Journal:
Proc. Amer. Math. Soc. 90 (1984), 5764
MSC:
Primary 40A15; Secondary 30B70
MathSciNet review:
722415
Fulltext PDF Free Access
Abstract 
References 
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Abstract: Necessary and sufficient conditions are given for a sequence to be a sequence of tails of a convergent continued fraction. Some special cases are also studied.
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, Functions defined by continued fractions. M eromorphic continuation (submitted).
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, Convergence of limit periodic continued fractions and of subsequences of their tails (in preparation).
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 [1]
 T. S. Chihara, Chain sequences and orthogonal polynomials, Trans. Amer. Math. Soc. 104 (1962), 116. MR 0138933 (25:2373)
 [2]
 , Orthogonal polynomials whose zeros are dense in intervals, J. Math. Anal. Appl. 24 (1968), 362371. MR 0232029 (38:355)
 [3]
 , Orthogonal polynomials whose distribution functions have finite point spectra, SIAM J. Math. Anal. 11 (1980) 358364. MR 559875 (81e:42032)
 [4]
 Lisa Jacobsen, Convergence acceleration for continued fractions , Trans. Amer. Math. Soc. 275 (1983), 265285. MR 678349 (84a:40002)
 [5]
 , A method for convergence acceleration of continued fractions , Lectures Notes in Math., 932, SpringerVerlag, Berlin and New York, 1982, pp. 7486.
 [6]
 , Further results on convergence acceleration for continued fraction , Trans. Amer. Math. Soc. (to appear).
 [7]
 , Functions defined by continued fractions. M eromorphic continuation (submitted).
 [8]
 , Convergence of limit periodic continued fractions and of subsequences of their tails (in preparation).
 [9]
 Lisa Jacobsen and Haakon Waadeland, Some useful formulas involving tails of continued fractions, Lecture Notes in Math., vol. 932, SpringerVerlag, Berlin and New York, 1982, pp. 99105. MR 690457 (84c:40004)
 [10]
 William B. Jones and Wolfgang J. Thron, Continued fractions: analytic theory and applications, Encyclopedia Math. Appl., No. 11, AddisonWesley, Reading, Mass., 1980. MR 595864 (82c:30001)
 [11]
 O. Perron, Die Lehre von den Kettenbrüchen, 3. Aufl., 2. Band, Teubuer, Stuttgart, 1957.
 [12]
 A. Pringsheim, Über die Konvergenz unendlicher Kettenbrüche, Bayer. Akad. Nat. Wiss. Kl. Sitz. Ber. 28 (1899), 295324.
 [13]
 W. J. Thron and Haakon Waadeland, Modifications of continued fractions, a survey, Lecture Notes in Math., vol. 932, SpringerVerlag, Berlin and New York, 1982, pp. 3866. MR 690452 (84j:30013)
 [14]
 , On a certain transformation of continued fractions, Lecture Notes in Math., vol. 932, SpringerVerlag, Berlin and New York, 1982, pp. 225240. MR 690464 (84c:30012)
 [15]
 H. S. Wall, Analytic theory of continued fractions, Chelsea, New York, 1967.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198407224155
PII:
S 00029939(1984)07224155
Keywords:
Continued fraction,
right tails,
wrong tails
Article copyright:
© Copyright 1984
American Mathematical Society
