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Continued Fractions of Tails of Hypergeometric Series

Borwein, Jonathan M. and Choi, Stephen and Pigulla, Wilfried (2005) Continued Fractions of Tails of Hypergeometric Series. American Mathematical Monthly, 112 . pp. 493-501.

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      Abstract

      The tails of the Taylor series for many standard functions such as $\arctan$ and $\log$ can be expressed as continued fractions in a variety ways. A surprising side effect is that some of these continued fractions provide a dramatic accelerations for the underlying power series. These investigations were motivated by a surprising observation about Gregory's series.

      Item Type: Article
      Additional Information: pubdom FALSE
      Subjects: 11-xx Number theory > 11Jxx Diophantine approximation, transcendental number theory
      33-xx Special functions
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 27 Oct 2003
      Last Modified: 12 Jan 2015 14:42
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/39

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