Article

The Ramanujan Journal

, Volume 24, Issue 1, pp 85-92

First online:

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

  • Michael D. HirschhornAffiliated withSchool of Mathematics and Statistics, UNSW Email author 

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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