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The Ramanujan Journal

, Volume 16, Issue 1, pp 83–95 | Cite as

Convergence and divergence of the Ramanujan AGM fraction

  • Lisa Lorentzen
Article

Abstract

We prove that the Ramanujan AGM fraction diverges if |a|=|b| with a 2b 2. Thereby we prove two conjectures posed by J. Borwein and R. Crandall. We also demonstrate a method for accelerating the convergence of this continued fraction when it converges.

Keywords

Convergence Continued fractions Ramanujan AGM-fraction 

Mathematics Subject Classification (2000)

40A15 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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