Converging factors for continued fractions 𝐾(𝑎_{𝑛}/1), 𝑎_{𝑛}→0

Gill, John

doi:10.1090/S0002-9939-1982-0633283-2

Converging factors for continued fractions $K(a_{n}/1)$, $a_{n}\rightarrow 0$
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Proc. Amer. Math. Soc. 84 (1982), 85-88 Request permission

Abstract:

Converging factors for continued fractions $K({a_n}/1)$ are used to enhance convergence either by accelerating the convergence process or by altering the region of convergence if the ${a_n}$’s are functions of a complex variable. The first results concerning the use of converging factors to accelerate convergence in the important case ${a_n} \to 0$ are presented in this paper.

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