Acta Mathematica Sinica, English Series

, Volume 27, Issue 12, pp 2301–2308 | Cite as

Factorizations that involve Ramanujan’s function k(q) = r(q)r2(q2)

Article

Abstract

In the “lost notebook”, Ramanujan recorded infinite product expansions for
$$\frac{1} {{\sqrt r }} - \left( {\frac{{1 - \sqrt 5 }} {2}} \right)\sqrt r and \frac{1} {{\sqrt r }} - \left( {\frac{{1 + \sqrt 5 }} {2}} \right)\sqrt r ,$$
, where r = r(q) is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan’s function k = k(q) = r(q)r2(q2).

Keywords

Infinite product Rogers-Ramanujan continued fraction Jacobi triple product identity 

MR(2000) Subject Classification

11F03 11F20 33E05 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.North Shore Mail CentreInstitute of Information and Mathematical Sciences, Massey University-AlbanyAucklandNew Zealand
  2. 2.School of Mathematics and StatisticsUNSWSydneyAustralia

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