O'Reilly logo

Elliptic Functions by W. F. Eberlein, J. V. Armitage

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

2 Jacobian elliptic functions of a complex variable

2.1 Introduction: the extension problem

In this chapter we define the Jacobian elliptic functions and establish their basic properties; for the convenience of the reader a summary of those properties is included at the end of the chapter.

In the last section of Chapter 1 we sought to make clear the possibility that the Jacobian elliptic functions (arising out of our study of the simple pendulum and as defined in (1.22) of that chapter) are much more than routine generalizations of the circular functions. But to explore their suspected richness it is necessary to move off the real line into the complex plane.

Our treatment is based on Abel’s original insight (1881), and is in three steps: (i) extension ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required