rational function

rational function

English

Noun

rational function (plural rational functions)

1. (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).
   • 1960, J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd Edition, American Mathematical Society, page 184,

     Our first problem is that of interpolation in prescribed points to a given function by a rational function whose poles are given.

   • 1970, Ellis Horowitz, Algorithms for Symbolic Integration of Rational Functions, University of Wisconsin–Madison, page 24,

     By Theorem 2.3.2., we have that the right-hand side of this equation can be equal to a rational function only if that rational function is equal to zero.

   • 2000, Alan F. Beardon, Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer, page 45,

     Let ${\\displaystyle {\\mathcal {C}}}$ be the class of continuous maps of ${\\displaystyle \\mathbb {C} _{\\infty }}$ into itself and let ${\\displaystyle {\\mathcal {R}}}$ be the subclass of rational functions. […] Now ${\\displaystyle {\\mathcal {R}}}$ is a closed subset of ${\\displaystyle {\\mathcal {C}}_{\\infty }}$ because if the rational functions ${\\displaystyle R_{n}}$ converge uniformly to ${\\displaystyle R}$ on the complex sphere, then ${\\displaystyle R}$ is analytic on the sphere and so it too is rational.

Hypernyms

• function, meromorphic function

Hyponyms

• proper rational function

Translations

function expressible as the quotient of polynomials

Finnish: rationaalifunktio German: rationale Funktion f Hungarian: racionális függvény (hu) Russian: рациона́льная фу́нкция f (racionálʹnaja fúnkcija) Turkish: rasyonel fonksiyon

References

• rational function on Wikipedia.Wikipedia