The Jacobian Elliptic Functions

Abstract

In Chapter 18, Ramanujan continues his development of the theory of elliptic functions begun in Chapter 16 with the theory of theta-functions and continued in Chapter 17 with an introduction to elliptic integrals and the compilation of a large catalog of series that can be evaluated in terms of elliptic function parameters. This chapter contains further series identities depending on the theory of elliptic functions. Such results are considerably fewer in number here than in Chapter 17 and generally are more difficult to prove. In particular, see Sections 4-7.