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
Famous quotes containing the words expression and/or ratio:
“The fact is, the public make use of the classics of a country as a means of checking the progress of Art. They degrade the classics into authorities. They use them as bludgeons for preventing the free expression of Beauty in new forms.”
—Oscar Wilde (1854–1900)
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
—Aldous Huxley (1894–1963)