Fundamental Properties of Elliptic Functions

Abstract

Chapter 17 is almost entirely devoted to the theory of elliptic functions. The groundwork was prepared in the sections on theta-functions in Chapter 16. In the present chapter, Ramanujan introduces Jacobian elliptic functions and elliptic integrals. It is interesting that Ramanujan does not use the classical notation and terminology from the theory of elliptic functions and integrals. In Section 6, we identify the functions and parameters employed by Ramanujan with the more familiar notations in the theory of elliptic functions.