On Some Ramanujan Identities for the Ratios of Eta-Functions - Bhargava, S.; Rajanna, K. R.; Vasuki, K. R. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
We give direct proofs of some of Ramanujan’s P-Q modular equations based on simply proved elementary identities from Chapter 16 of his Second Notebook.