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A result on nearness of functions and their regular $ C$-fraction expansions


Authors: Lisa Jacobsen and Haakon Waadeland
Journal: Proc. Amer. Math. Soc. 106 (1989), 741-750
MSC: Primary 30B70; Secondary 40A15
DOI: https://doi.org/10.1090/S0002-9939-1989-0967487-2
MathSciNet review: 967487
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Abstract: We shall prove a "nearness"-result of the following type. If $ f(w)$ is a holomorphic function in $ \Omega = \{ w \in {\mathbf{C}};\left\vert {\arg (1 + 4w)} \right\vert < \pi \} $ and "sufficiently near" the function $ (\sqrt {1 + 4w} - 1)/2$, then $ f(w)$ has a regular C-fraction expansion $ K({a_n}w/1)$ where $ {a_n} \to 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0967487-2
Keywords: Continued fractions, $ {\text{C}}$-fractions, regular $ {\text{C}}$-fractions, $ {\text{C}}$-fraction expansions
Article copyright: © Copyright 1989 American Mathematical Society

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