The Ramanujan Journal

, Volume 24, Issue 1, pp 85–92

On the 2- and 4-dissections of Ramanujan’s continued fraction and its reciprocal

Article

Abstract

We present elementary proofs, using only Jacobi’s triple product identity, of four identities of Ramanujan and eight identities of Hirschhorn relating to the 2-dissection and the 4-dissection of Ramanujan’s continued fraction and its reciprocal, and of two identities from Ramanujan’s famous list of forty.

Keywords

2-dissection 4-dissection Ramanujan’s continued fraction List of forty 

Mathematics Subject Classification (2000)

11A55 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUNSWSydneyAustralia

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