The Ramanujan Journal

, Volume 24, Issue 1, pp 85–92

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

Authors

    • School of Mathematics and StatisticsUNSW
Article

DOI: 10.1007/s11139-010-9272-z

Cite this article as:
Hirschhorn, M.D. Ramanujan J (2011) 24: 85. doi:10.1007/s11139-010-9272-z

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

Copyright information

© Springer Science+Business Media, LLC 2010