Expression As A Ratio of Polynomials
For even orders, the elliptic rational functions may be expressed as a ratio of two polynomials, both of order n.
- (for n even)
where are the zeroes and are the poles, and is a normalizing constant chosen such that . The above form would be true for odd orders as well except that for odd orders, there will be a pole at x=∞ and a zero at x=0 so that the above form must be modified to read:
- (for n odd)
Read more about this topic: Elliptic Rational Functions
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