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 
Similar Articles 
Additional Information
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.
 [1]
T.
S. Chihara, Chain sequences and orthogonal
polynomials, Trans. Amer. Math. Soc. 104 (1962), 1–16. MR 0138933
(25 #2373), http://dx.doi.org/10.1090/S00029947196201389337
 [2]
T.
S. Chihara, Orthogonal polynomials whose zeros are dense in
intervals, J. Math. Anal. Appl. 24 (1968),
362–371. MR 0232029
(38 #355)
 [3]
T.
S. Chihara, Orthogonal polynomials whose distribution functions
have finite point spectra, SIAM J. Math. Anal. 11
(1980), no. 2, 358–364. MR 559875
(81e:42032), http://dx.doi.org/10.1137/0511033
 [4]
Lisa
Jacobsen, Convergence acceleration for continued
fractions 𝐾(𝑎_{𝑛}/1), Trans. Amer. Math. Soc. 275 (1983), no. 1, 265–285. MR 678349
(84a:40002), http://dx.doi.org/10.1090/S00029947198306783491
 [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, Analytic theory of continued fractions (Loen, 1981)
Lecture Notes in Math., vol. 932, Springer, Berlin, 1982,
pp. 99–105 (English, with Russian summary). MR 690457
(84c:40004)
 [10]
William
B. Jones and Wolfgang
J. Thron, Continued fractions, Encyclopedia of Mathematics and
its Applications, vol. 11, AddisonWesley Publishing Co., Reading,
Mass., 1980. Analytic theory and applications; With a foreword by Felix E.
Browder; With an introduction by Peter Henrici. 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,
Analytic theory of continued fractions (Loen, 1981) Lecture Notes in
Math., vol. 932, Springer, Berlin, 1982, pp. 38–66. MR 690452
(84j:30013)
 [14]
W.
J. Thron and Haakon
Waadeland, On a certain transformation of continued fractions,
Analytic theory of continued fractions (Loen, 1981) Lecture Notes in
Math., vol. 932, Springer, Berlin, 1982, pp. 225–240. MR 690464
(84c:30012)
 [15]
H. S. Wall, Analytic theory of continued fractions, Chelsea, New York, 1967.
 [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.
Similar Articles
Retrieve articles in Proceedings 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/S00029939198407224155
PII:
S 00029939(1984)07224155
Keywords:
Continued fraction,
right tails,
wrong tails
Article copyright:
© Copyright 1984 American Mathematical Society
