rational function
Noun
Meaning
rational function (plural rational functions)
(mathematics, complex analysis, algebraic geometry) Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator).
Examples
Asymptotes for rational functions A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes.
Green: difference between the graph and its asymptote for When the numerator of a rational function has degree exactly one greater than the denominator, the function has an oblique (slant) asymptote.
Generally, this works for any product wherein each factor is a rational function of the index variable, by factoring the rational function into linear expressions.
Julia set (in white) for the rational function associated to Newton's method for f : z→z 3 −1.
New proof of the theorem that every integral rational function of one variable can be represented as a product of linear functions of the same variable).
The complexity of any such filter is given by the order N, which describes the order of the rational function describing the frequency response.