The Ramanujan Journal

, 20:311 | Cite as

On Ramanujan’s function k(q)=r(q)r2(q2)



In both his second and lost notebooks, Ramanujan introduced a function, related to the Rogers–Ramanujan continued fraction and its quadratic transformation, and listed several of its properties. We extend these results and develop a systematic theory.


Atkin-Lehner involution Eisenstein series Eta-function Ramanujan’s lost notebook Ramanujan’s second notebook Rogers-Ramanujan continued fraction Theta function 

Mathematics Subject Classification (2000)

11F11 11F20 14K25 33D52 33E05 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.IIMSMassey University-AlbanyAucklandNew Zealand

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