A Note on Cubic Modular Equations of Degree Two * M. S. Mahadeva Naika † Department of Mathematics, Bangalore University, Central College Campus Bangalore 560 001, Karnataka State, India Received June 23, 2004, Accepted January 14, 2005. Abstract On Page 259 of his second notebook [3], Ramanujan recorded many cubic modular equations of degree 2. In this paper we establish several cubic modular equations of degree 2 akin to those in Ramanujan’s work. As an application of our results, we also establish some new P - Q eta- function identities. Keywords and Phrases: Cubic modular equations, Eta-function identities. Tamsui Oxford Journal of Mathematical Sciences 22(1) (2006) 1-8 Aletheia University 1. A Family of Cubic Modular Equations The ordinary hypergeometric series 2 F 1 (a,b; c; x) is defined by 2 F 1 (a,b; c; x)= ∞  n=0 (a) n (b) n x n (c) n , * 2000 Mathematics Subject Classification. Primary 33D15, 33D20; Secondary 11S23. † E-mail: msmnaika@rediffmail.com brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by ePrints@Bangalore University