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Convergence and divergence of the Ramanujan AGM fraction

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Abstract

We prove that the Ramanujan AGM fraction diverges if |a|=|b| with a 2≠b 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.

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  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Lisa Lorentzen

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  1. Lisa Lorentzen
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Correspondence to Lisa Lorentzen.

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Lorentzen, L. Convergence and divergence of the Ramanujan AGM fraction. Ramanujan J 16, 83–95 (2008). https://doi.org/10.1007/s11139-007-9112-y

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  • DOI: https://doi.org/10.1007/s11139-007-9112-y

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