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Separate convergence of general $ {\rm T}$-fractions


Author: W. J. Thron
Journal: Proc. Amer. Math. Soc. 111 (1991), 75-80
MSC: Primary 40A15
DOI: https://doi.org/10.1090/S0002-9939-1991-1045151-0
MathSciNet review: 1045151
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Abstract | References | Similar Articles | Additional Information

Abstract: This article is concerned with the separate convergence of the sequences of numerators $ \{ {A_n}(z)\} $ and denominators $ \{ {B_n}(z)\} $ of the approximants $ {A_n}(z)/({B_n}(z)$ of the general $ {\text{T}}$-fraction

$\displaystyle \mathop K\limits_{n = 1}^\infty \left( {\frac{{{F_n}z}}{{1 + {G_n}z}}} \right).$

Convergence results for sequences $ \{ {A_n}(z)/{\Gamma _n}(z)\} $ and $ \{ {B_n}(z)/{\Gamma _n}(z)\} $, where the sequence $ \{ {\Gamma _n}(z)\} $ is "sufficiently simple" are also derived.

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

  • [1] Lisa Jacobsen, A note on separate convergence for continued fractions, submitted.
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  • [3] H. M. Schwartz, A class of continued fractions, Duke Math. J. 6 (1940), 48-65. MR 0001321 (1:217e)
  • [4] W. J. Thron, Some results on separate convergence of continued fractions, Lecture Notes in Math. (to appear) MR 1071773 (91m:30006)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045151-0
Keywords: Continued fractions, general $ {\text{T}}$-fractions, separate convergence
Article copyright: © Copyright 1991 American Mathematical Society

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