## 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, - 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

*Some convergence regions for a continued fraction*, Dissertation, Univ. of Texas, Austin, 1950.

## 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