Algorithm

In this section we implement the elliptic rational functions in Mathematica.

Elliptic Rational Functions

First, we define the first-order function .

We use the nesting property and the closed-form expressions [4] for orders .

We use the Jacobi elliptic function JacobiSN and the complete elliptic integral of the first kind EllipticK for orders .

Discrimination Factor

The first-order discrimination factor equals the selectivity factor.

We use the nesting property and the closed-form expressions [4] for orders .

We use the Jacobi elliptic function JacobiSN and the complete elliptic integral of the first kind EllipticK for orders .

Zeros and Poles

The zeros and poles of for orders are computed in terms of the Jacobi elliptic function JacobiSN and the complete elliptic integral of the first kind EllipticK.

Closed-form expressions for the zeros and poles of exist [4] for orders and these formulas do not require Jacobi functions.

Traditional Forms