Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities

Abstract

In several ways, this is a remarkable chapter. Not only are the results enormously interesting and often difficult to prove, but many questions arise in regard to Ramanujan's methods of proof. Undoubtedly, many of the proofs given here are quite unlike those found by Ramanujan. He evidently possessed methods that we have been unable to discern. No hints whatsoever of his methods are provided by Ramanujan.