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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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


Author: W. J. Thron
Journal: Proc. Amer. Math. Soc. 111 (1991), 75-80
MSC: Primary 40A15
MathSciNet review: 1045151
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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.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045151-0
PII: S 0002-9939(1991)1045151-0
Keywords: Continued fractions, general $ {\text{T}}$-fractions, separate convergence
Article copyright: © Copyright 1991 American Mathematical Society