Elliptic rational functions are a special class of rational
functions that have nice properties for approximating other functions over the
interval .
In particular, they are equiripple, satisfy over , are minimax
approximations over , exhibit monotonic increase on , and have minimal order . Additional properties include symmetry

(1)

normalization

(2)

the property

(3)

and the nesting property

(4)

(Lutovac et al. 2001).

Letting the discrimination factor be the largest value of for , the elliptic rational functions can be defined by