Nesting Property

Higher-order elliptic rational functions can be generated from lower-order functions by using the nesting property [4]

For example, .

The corresponding nesting formula can be derived for the zeros and poles of as shown in [4]. For the zeros and poles of can be expressed symbolically in terms of without using the Jacobi elliptic functions. Here is an example.

For orders , cannot be expressed symbolically without the Jacobi elliptic functions or the like.