Twin-convergence regions for continued fractions $K(a_{n}/1)$
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- by William B. Jones and W. J. Thron
- Trans. Amer. Math. Soc. 150 (1970), 93-119
- DOI: https://doi.org/10.1090/S0002-9947-1970-0264043-9
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References
- J. D. Bankier and Walter Leighton, Numerical continued fractions, Amer. J. Math. 64 (1942), 653–668. MR 7070, DOI 10.2307/2371711 George Copp, Some convergence regions for a continued fraction, Dissertation, Univ. of Texas, Austin, 1950.
- V. F. Cowling, Walter Leighton, and W. J. Thron, Twin convergence regions for continued fractions, Bull. Amer. Math. Soc. 50 (1944), 351–357. MR 10624, DOI 10.1090/S0002-9904-1944-08142-1
- T. F. Glass and Walter Leighton, On the convergence of a continued fraction, Bull. Amer. Math. Soc. 49 (1943), 133–135. MR 7803, DOI 10.1090/S0002-9904-1943-07874-3
- Peter Henrici and Pia Pfluger, Truncation error estimates for Stieltjes fractions, Numer. Math. 9 (1966), 120–138. MR 212991, DOI 10.1007/BF02166031
- K. L. Hillam and W. J. Thron, A general convergence criterion for continued fractions $K(a_{n}/b_{n})$, Proc. Amer. Math. Soc. 16 (1965), 1256–1262. MR 193393, DOI 10.1090/S0002-9939-1965-0193393-3
- William B. Jones and R. I. Snell, Truncation error bounds for continued fractions, SIAM J. Numer. Anal. 6 (1969), 210–221. MR 247737, DOI 10.1137/0706019
- William B. Jones and W. J. Thron, Convergence of continued fractions, Canadian J. Math. 20 (1968), 1037–1055. MR 230888, DOI 10.4153/CJM-1968-101-3
- L. J. Lange, On a family of twin convergence regions for continued fractions, Illinois J. Math. 10 (1966), 97–108. MR 186798, DOI 10.1215/ijm/1256055205
- L. J. Lange and W. J. Thron, A two-parameter family of best twin convergence regions for continued fractions, Math. Z. 73 (1960), 295–311. MR 116092, DOI 10.1007/BF01215312
- Walter Leighton and W. J. Thron, On the convergence of continued fractions to meromorphic functions, Ann. of Math. (2) 44 (1943), 80–89. MR 7805, DOI 10.2307/1969066
- Walter Leighton and H. S. Wall, On the Transformation and Convergence of Continued Fractions, Amer. J. Math. 58 (1936), no. 2, 267–281. MR 1507150, DOI 10.2307/2371036
- Oskar Perron, Über zwei Kettenbrüche von H. S. Wall, Bayer. Akad. Wiss. Math.-Nat. Kl. S.-B. 1957 (1957), 1–13 (German). MR 0106371
- Vikramaditya Singh and W. J. Thron, A family of best twin convergence regions for continued fractions, Proc. Amer. Math. Soc. 7 (1956), 277–282. MR 77678, DOI 10.1090/S0002-9939-1956-0077678-1
- W. J. Thron, Two families of twin convergence regions for continued fractions, Duke Math. J. 10 (1943), 677–685. MR 9214, DOI 10.1215/S0012-7094-43-01063-4
- W. J. Thron, A family of simple convergence regions for continued fractions, Duke Math. J. 11 (1944), 779–791. MR 11746, DOI 10.1215/S0012-7094-44-01166-X
- W. J. Thron, Zwillingskonvergenzgebiete für Kettenbrüche $1+K(a_{n}/1)$, deren eines die Kreisscheibe $|a_{2n-1}|\leq \rho ^{2}$ ist, Math. Z. 70 (1958/59), 310–344 (German). MR 105488, DOI 10.1007/BF01558596
- W. J. Thron, Convergence of sequences of linear fractional transformations and of continued fractions, J. Indian Math. Soc. (N.S.) 27 (1963), 103–127 (1964). MR 183855
- W. J. Thron, On the convergence of the even part of certain continued fractions, Math. Z. 85 (1964), 268–273. MR 168960, DOI 10.1007/BF01112148
- H. S. Wall, Partially bounded continued fractions, Proc. Amer. Math. Soc. 7 (1956), 1090–1093. MR 82953, DOI 10.1090/S0002-9939-1956-0082953-0
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 93-119
- MSC: Primary 30.25
- DOI: https://doi.org/10.1090/S0002-9947-1970-0264043-9
- MathSciNet review: 0264043