Jacobi Elliptic Functions

Introduction

There are many definitions for the Jacobi elliptic functions. We refer the reader to ​DLMF 22.2 for more information on definitions.

However, in our definitions, we use the parameter m instead of the modular angle alpha or the modulus k. These are related by the following expressions:

  m = k^2
  m = sin(alpha)

Sn

(jacobi-sn u m)

Jacobi sn function

Cn

(jacobi-cn u m)

Jacobi cn function

Dn

(jacobi-dn u m)

Jacobi dn function

References

• ​DLMF Jacobian Elliptic Functions
• ​A&S 16