Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A convergence theorem for limitärperiodisch $ T$-fractions of rational functions

Author: Kari Hag
Journal: Proc. Amer. Math. Soc. 32 (1972), 491-496
MSC: Primary 30A22
MathSciNet review: 0291421
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a limitärperiodisch T-fraction, which corresponds to a rational function, converges (locally uniformly) to the original function in a certain domain.

References [Enhancements On Off] (What's this?)

  • [1] K. Hag, A theorem on T-fractions corresponding to a rational function, Proc. Amer. Math. Soc. 25 (1970), 247-253. MR 41 #3723. MR 0259081 (41:3723)
  • [2] W. B. Jones, Contributions to the theory of Thron continued fractions, Ph.D. Thesis, Vanderbilt University, Nashville, Tennessee, 1963, 68 pp.
  • [3] W. B. Jones and W. J. Thron, Further properties of T-fractions, Math. Ann. 166 (1966), 106-118-MR 34 #319. MR 0200425 (34:319)
  • [4] O. Perron, Die Lehre von den Kettenbrüchen, Verbesserte und erweiterte Aufl., Band II, Analytisch-funktionentheoretische Kettenbrüche, Teubner Verlagsgesellschaft, Stuttgart, 1957. MR 19, 25. MR 0085349 (19:25c)
  • [5] W. J. Thron, Some properties of continued fractions $ 1 + {d_0}z + K(z/(1 + {d_n}z))$, Bull. Amer. Math. Soc. 54 (1948), 206-218. MR 9, 508. MR 0024528 (9:508c)
  • [6] H. Waadeland, On T-fractions of functions holomorphic and bounded in a circular disc, Norske Vid. Selsk. Skr. (Trondheim) 1964, no. 8, 19 pp. MR 31 #1364. MR 0177100 (31:1364)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A22

Retrieve articles in all journals with MSC: 30A22

Additional Information

Keywords: Continued fractions corresponding to power series, convergence of continued fractions, T-fraction expansion, limitärperiodisch T-fraction
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society